摘要:

THE RQYAL SOCIETY OF CHEMISTRY Journal of the Chemical Society Faraday Transactions Scientific Editor Dr. Peter J. Sarre Department of Chemistry University of Nottingham University Park Nottingham NG7 2RD, UK Faraday Editorial Board Prof. I.W. M.Smith (Birmingham) (Chairman) Prof. M. N. R. Ashfold (Bristol) Dr. 6. E. Hayden (Southampton) Dr. D. C. Clary (Cambridge) Prof. A. R. Hillman (Leicester) Dr. L. R. Fisher (Bristol) Prof. J. Holzwarth (Berlin) Prof. H. M. Frey (Reading) Dr. P. J. Sarre (Nottingham) Dr. R. K. Thomas (Oxford) Editorial Manager and Secretary to Faraday Editorial Board Dr. Robert J. Parker The Royal Society of Chemistry Thomas Graham House Science Park Milton Road Cambridge CB4 4WF, UK Staff Editor: Dr. R.A. Whitelock Senior Assistant Editor: Mrs. S. Shah Assistant Editors: Dr. L. Milne, Mrs. C. J. Seeley Editorial Secretary: Mrs. J. E. Gibbs International Advisory Editorial Board R. S. Berry (Chicago) Y. Marcus (Jerusalem) A. M. Bradshaw (Berlin) B. J. 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Full details of the form of manuscripts for Articles and Faraday Communications, con- ditions for acceptance etc. are given in issue number one of Faraday Transactions, published in January of each year, or may be obtained from the Editorial Manager. There is no page charge for papers published in Faraday Transactions. Fifty reprints are supplied free of charge. Dr. P. J. Sarre, Scientific Editor. Tel.: Nottingham (0602) 513465 (24 hours) E- Mail (JANET): PCZPSF(d U K.AC.NOTT.VAX Fax: (0602) 513466 Telex: 37346 UNINOT G Dr. R. J. Parker, Editorial Manager. Tel. : Cambridge (0223) 420066 E-Mail (INTERNET): RSCl (aRSC.ORG (For access from JANET use RSCl %RSC.ORG@ UK.AG.NSF N ET- R ELAY) Fax : (0223) 423623 or 420247 Telex: 81 8293 ROYAL G

ISSN:0956-5000    

DOI:10.1039/FT99490FX045

出版商:RSC    

年代:1994

数据来源: RSC

摘要:

Dirhodium(i1) Te tra a ce ta te Ca ta ly se d Hydro b ora tion of A lken es A New Route to Cyclic lodonium Hides Photochemical Production of Tetra valent Americium in Hydrogencarbonate-Carbonate Media New Methods for the Synthesis of Petfluorooxaziridines Electron Tunneling in Heterogeneous Catalysis. Superoxide Anion Radical Decay on Palladium Promoted Yflria Subsequent Peripheral Cyclopropanation as a Synthetic Approach to Cyclic and Cyclo-substituted Triangulanes Total Synthesis of the Archaebacterial C,,-Diol and its Enantiomer Based on (R)-5-Acetoxy4-methylpentanoic Acid An Efficient Synthesis of (S,Z)-Dodec-3-en-ll-olide(Ferrulactone Il) using 2-Carboxyethyltriphenylphosphonium Bromide Reaction of Trichloromethylarenes with Pyridine: A Novel Synthesis of N-(4-Pyridyl)pyridinium Salts and Aromatic Aldehydes Photochromic Behaviour of Non-transition Metal Chelate Complexes of Salicylaldimines Synthesis of Chromophores Based on Porphyrins and Open-chain Polypyrroles 3,4-Dinitrofuroxan-the First Example of a Pernitro Heterocycle New Intercalation Compounds of Molybdenum Disulfide with Transition metals Lower Oxidation States of Protactinium Photoionisation and Photoluminescence of Luminol in Aqueous Solution A Novel Mononuclear Tungsten(v1) Complex with 1-Hydroxyethylenediphosphonic Acid, Exhibiting a W03 Core Pressure Tensor and Local Density Profiles of Computer-simulated Water Clusters Registration Method for Metastable Decomposition of Benzene-Arn and Toluene-Arn Cluster Ions in RETOF Instruments Unusual Isotope Effect Induced by Photolysis of Uranyl Salts in Micelles Synthesis of Fluorinated 4H-1,4-Benzothiazine-2-carboxylic Acid 1,1-Dioxides-Thionated Analogues of Pefloxacin Natural Abundance Solid State 2H NMR Studies of Phase Transitions in Rotator Phase Solids Giant Pd Clusters observed by High Resolution Electron Microscopy HAZARDS IN THE CHEMICAL LABORATORY 5th Edition ‘.easy to read, an excellent reference text, and a worthwhile investment.’ Journal of the American Chemical Society reviewing the 4th Edition. The new edition of this essential laboratory handbook is the ‘key’ requirement for all research, development, production, analytical and teaching laboratories worldwide. The 5th Edition provides: New features include: expanded ‘Yellow Pages’ section on 0 a quick guide to the hazardous properties of 1339 substances (over 800 more than were hazardous substances, providing immediate covered in the previous edition) information on hazardous properties, 0 details of the latest UK and EC regulations recommended control procedures and safety measures 0 an extremely useful emergency action check 0list -users can fill in their own key contacts for complete guide to labelling requirements to hospitals, fire etc.comply with EC directives and UK legislation, including the risk and safety phrases that must 0 handy tables, syrnbck and statistics for ease appearof reference 0 chapter on electrical hazards 0 a description of the American scene, including 0US legislation and safety practices -index to ‘Yellow Pages’ section, with highlighting differences between the UWEC synonyms of compounds and USA index to CAS Registry Numbers 0 PVC Protective Binding xx + 676 pages ISBN 0 85186 229 2 (1992) Price €45.00 If you have not yei ordered your copy of the NEW edition, do so now! Why take chances? Be informed and safe. To order, please contact: ROYALIRoyal Society of Chemistry, Turpin Distribution # SOCIETYOF Services Ltd,- Blackhorse Road,-Letchworth, CHEMISTRY InformationHerts SG6 IHN, United Kingdom. Services Telephone: +44 (0)462 672555 Fax: +44 (0)462 486947. II 0956-5000(199L112 1-2

ISSN:0956-5000    

DOI:10.1039/FT99490BX047

出版商:RSC    

年代:1994

数据来源: RSC

摘要:

ISSN 0956-5000 JCFTEV(12) 1559-1 81 0 (1994) JOURNAL OF THE CHEMICAL SOCIETY Faraday Transactions Physical Chemistry & Chemical Physics A Symposium on Potential-energy Surfaces and Organic Reaction Paths was held at the University of Oxford on the 15th, 16th and 17th December 1993. CONTENTS 1559 Introductory Lecture: Electrostatic acceleration of the 1,5-H shifts in cyclopentadiene and in penta-1,3-diene by Li + complexation: Aromaticity of the transition structures H. Jiao and P. von Rague Schleyer 1569 Some thoughts on reaction-path following H. B. Schlegel 1575 Prediction of whole reaction paths for large molecular systems S. S-L. Chiu, J. J. W. McDouall and I. H. Hillier 1581 What Woodward and Hoffmann didn’t tell us : The failure of the Born-Oppenheimer approximation in competing reaction pathways G.C. G. Waschewsky, P. W. Kash, T. L. Myers, D. C. Kitchen and L. J. Butler 1599 Concerted and stepwise mechanisms in cycloaddition reactions : Potential surfaces and isotope effects K. N. Houk, Y. Li, J. Storer, L. Raimondi and B. Beao 1605 General Discussion 1617 Ab initio MC-SCF study of thermal and photochemical [2 + 2) cycloadditions F. Bernardi, A. Bottoni, M. Olivucci, A. Venturini and M. A. Robb 1631 Transition states, avoided crossing states and valence-bond mixing: Fundamental reactivity paradigms S. Shaik and A. C. Reddy 1643 Spin-coupled description of organic reaction pathways : The cycloaddition reaction of two ethene molecules P. B. Karadakov, J. Gerratt, D. L. Cooper and M.Raimondi 1653 Photophysics and potential-energy hypersurfaces of permethylated oligosilanes H. S. Plitt, J. W. Downing, M. K. Raymond, V. Balaji and J. Michl 1663 Stereoselectivity and regioselectivity in Diels-Alder reactions studied by intermolecular perturbation theory S. L. Craig and A. J. Stone 1669 General Discussion 1681 Inverted potential-energy surfaces in the radical-cation Cope rearrangements of hexa- 1,5-diene and semibullvalene F. Williams 1689 Potential surfaces for cyclopropane stereomutations : What a difference geminal fluorines make S. J. Getty, D. A. Hrovat, J. D. Xu, S. A. Barker and W. T. Borden 1703 Theoretical kinetic isotope effects for the hydride-transfer step in lactate dehydrogenase J. An&& V. Moliner and V. S.Safoat 1709 Transition-state structural variation and mechanistic change J. A. Barnes,J. Wilkie and I. H. Williams 1715 Variational transition-state theory and semiclassical tunnelling calculations with interpolated corrections : A new approach to interfacing electronic structure theory and dynamics for organic reactions W. P. Hu, Y-P.Liu and D. G. Truhlar 1727 Investigation of solvent effects on pericyclic reactions by computer simulations W. L. Jorgensen, J. F. Blake, D. Lim and D. L. Severance 1733 General Discussion 1745 Importance of water in aldol condensation reactions of acetaldehyde E. L. Coitiiio, J. Tomasi and 0.N. Ventura 1757 Transition structures of the Friedel-Crafts reaction in solution I. Tuiion, E. Silla and J.Bertran 1763 Phosphate ester hydrolysis :Calculation of gas-phase reaction paths and solvation effects A. Dejaegere, X. Liang and M. Karplus 1771 Ring-chain rearrangements of phosphirane M. T. Nguyen, L. Landuyt and L. G. Vanquickenborne 1783 Molecular orbital studies of electron-transfer reactions G. Rauhut and T. Clark 1789 Theoretical studies of nucleophilic additions of monomeric and dimeric organometallics M. Nakamura, E. Nakamura, N. Koga and K. Morokuma 1799 General Discussion Note: Where an asterisk appears against the name of one or more of the authors, it is included with the authors’ approval to indicate that correspondence may be addressed to this person. COPIES OF CITED ARTICLES The Royal Society of Chemistry Library can usually supply copies of cited articles. For further details contact: The Library, Royal Society of Chemistry, Burlington House, Piccadilly, London W 1V OBN, UK Tel: 44 (0)71-437 8656 Fax: +44 (0)71-287 9798 Telecom Gold 84:BUR210 Electronic Mailbox (Internet) LIBRARY @RSC.ORG. If the material is not available from the Society’s Library, the staff will be pleased to advise on its availability from other sources. Please note that copies are not available from the RSC at Thomas Graham House, Cambridge.

ISSN:0956-5000    

DOI:10.1039/FT99490FP115

出版商:RSC    

年代:1994

数据来源: RSC

摘要:

List of Posters Why is SiH,- a ‘stable’ intermediate, whereas CH,- is a transition state? The spin-coupled point of view T. P. Cunningham, D. L. Cooper, J. Gerratt, P. B. Karadakov and M. Raimondi, University of Liverpool, University of Bristol, UK, University of Milan, Italy Catalytic chemistry of furan and thiophene. Ab initio calculations using the spin-coupled valence bond method of the inter- action of furan and thiophene with a positive centre P. C. H. Mitchell University of Reading, UK, J. Gerratt and G. M. Ram, University of Bristol, UK Ab initio SCF-MO model of the HC0,-/H,O exchange in carbonic anahydrase J. L. Andres, M. Sola and M. Duran, Uni-versity of Girona, Spain, A. Lledos and J. Bertran, Universitat Autonoma de Barcelona, Belatera, Catalonia, Spain Potential-energy surfaces for the hydrolysis of a model of adeonosine monophosphate J.A. Barnes and I. H. Williams, University of Bath, UK Solvent effects on Diels-Alder revisited : Ab initio computations using the self-consistent reaction field approach L. Salvatella, R. M. Martinez, J. I. Garcia, J. A. Mayoral, X. Assfeld and M. F. Ruiz-Lopez, University of Zaragoza, Spain and University of Nancy I, France The Hammond postulate revisited : The relationship between potential-energy surface curvature and transition structure position M. M. Franc1 Bryn Mawr College, USA Ab initio calculations on 2,3-dihydro- 1,6diazepinium cation R. Zwaans and C. Thomson University of St Andrews, UK Hydron-transfer reactions between carbon and oxygen H.F. Koch, Ithaca College, USA The automerization of benzene : Group theoretical considerations R. G. A. Bone, Molecular Research Institute, Palo Alto, USA Semiempirical calculation of kinetic isotope effects on the Menschutkin reactions E. Gawlita and P. Paneth Technical Uni- versity of Lodz, Poland Enzyme catalysis and transition structure in vacuo. Rubisco’s enolization, carboxylation and oxygenation reactions 0.Tapia, Uppsala University, Sweden, J. Andres and V. S. Salfont, Universitat Jaume I, Castello, Spain The Claisen rearrangement of chorismate, an ab initio study 0. Wiest and K. N. Houk, University of California, Los Angeles USA Solvent effect on the conformational behaviour of substituted spiro[4,5] decanes and spiro[5,5] undecanes S.Erdem, T. Varnali, V. Aviyente and M. F. Ruiz-Lopez, Bogazici University, Istanbul, Turkey and Uniuersity of Nancy, France Reaction of phosphaethene (H,C=PH) with hydrogen isocyanide (HN=C): [2 + 21 vs. [2 + 13 cycloaddition? A. Van Keer, M. T. Nguyen and L. G. Vanquickenborne, Leuven University, Heverlee, Belgium Molecular mechanics calculations of conformational ring inversion potential in heterocyclic cis-decalins and stereoelectronic implications. Oxa systems L. Golender, H. Senderowitz and B. Fuchs, Tel-Aviv University, Israel Potential-energy surfaces for SiH, addition reactions from kinetic studies N. Al-Rubaiey, R. Becarfa, H. M. Frey, B. P.Mason and R. Walsh University of Reading, UK, Transition state structural variations in the Menshutkin reaction.Computational study of steric and electronic substituent effects U. Berg, M. Chanon, R. Gallo and M. Rajzmann, University of Aix-Marseille III, France and University of Lund, Sweden Cisltrans isomerisation: Stilbene and 1,3-diphenylallyl ions B. Brocklehurst, C. E. Oliver, B. T. Pickup and R. N. Young, University of Shefjield, UK Theoretical investigation of dimerization and trimerization of alkene radical cations J. W. Alvarez-Idaboy, L. A. Eriksson, N. Salhi, T. Fangstrom and S. Lunell, Uppsala University, Sweden MOPLOT: A convenient interactive visualisation tool for quantum chemistry S. Matzinger and T. Bally, University of Friborg, Switzerland Acceleration of DDRP method by potential-energy transformations L. L. Stacho, G. Domotor and M.I. Ban, Attila Jozsef University, Hungary IRCs for some collinear reactions calculated by the DDRP method T. Kortvelyesi, Gy. Domotor M. I. Ban and L. L. Stacho, Attila Jozsef University, Hungary Studies of reaction pathways and transition structures using spin-coupled theory J. K. Gregory, G. Ram, P. B. Karadakov and J. Gerratt, University of Bristol, UK, D. L. Cooper, University of Liverpool, UK, M. Raimondi, Uniuersity of Milan, Italy The mechanisms of rearrangement of nitro cyclohexadienones J. H. Ridd and S. Trevellick, University College, London, UK, J. P. B. Sandall, University of Exeter, UK The role of vicinal delocalizations in controlling the regiochemistry of the cycloaddition of diazomethane and formonitrile oxide to methylvinylethene, acrylonitrile and propene A.Rastelli and M. Bagatti, University of Modena, Italy, R. Gandolfi and M. Burdisso, University of Pavia, Italy 1 Proton transfer in liquid water F. R. Tortonda, J. L. Pascual-Ahuir, E. Silla and I. Tuiion University of Valencia, Spain Excited state cisltrans isomerization pathways in short polyenes: A CASSCF computational study M. Olivucci and F. Ber-nardi, University of Bologna, Italy, M. A. Robbs, King's College, London, UK On the use of ab initio quantum molecular similarities to understand organic reactions better M. Sola, J. Metres, R. Carbi, and M. Duran, University of Girona, Spain An ab initio investigation of identity-reaction proton transfers from acetaldehyde and acetonitrile to their respective conjugate bases W.H. Saunders Jr and J. E. Van Verth, University of Rochester, USA Regioselectivity in the electrophilic addition of aldehydes to lithium gem-dichloroallyl C. Canepa and G. Tonachini, Universityof Turin, Italy Solvent effect computations using an improved continiuum model based on a general definition of the cavity. An Ab initio analysis of the hydrolysis of formamide V. Dillet and S. Antonczak, University of Nancy, France Numerical calculation of gradient extremals W. Quapp, 0.Imig and D. Heidrich, University of Leipzig, Germany A theoretical study of the activation energy of the reaction H,O + 'OH +HO' + H,O: Tunnelling contributions M. R. Hand and I. H. Williams, University of Bath, UK, G. G. Baht-Kurti, University of Bristol, UK Theoretical modelling of the reduction of acetone by chiral oxaborolidine-borane adducts L.P. Linney, I. H. Williams and C. R. Self, University of Bath and Roche Research Centre, Welwyn Garden City, UK Conformational equilibrium of a, unsaturated carbonyl compounds in solution. A SCRF-DFT study X. Assfeld, F. Bohr and M. F. Ruiz-Lopez, University of Nancy, France The mechanisms of electrophilic substitutions of aliphatic hydrocarbons: CH, + NO' P. R. Schreiner, P. von Rag& Schleyer and H. F. Schaefer 111, University of Georgia, Athens, USA and University of Erlangen-Nurnberg, Germany Semiempirical calculation of the oxygen isotope effect on the binding of oxamate to lactate dehydrogenase E. Gawlita, V. Anderson and P. Paneth, Technical University Sodz, Poland and Case Western Reserve University, USA An ab initio study of the solvent effect on the rotational barrier of 2-cyano-1, 1-dihydroxyethane V.Aviyente, T. Varnali and M. F. Ruiz-Lopez, Bogazici University, Istanbul, Turkey and University of Nancy, France The spin-coupled interpretation of CASSCF wave functions T. Thorsteinsson and D. L. Cooper, University of Liverpool, UK, J. Gerratt, University of Bristol, UKand M. Raimondi, University of Milan, Italy The ketene-oxirene isomerization hypersurface G. Vacek, J. M. Galbraith, Y. Yamaguchi, H. F. Schaefer 111, A. Scott, R. H. Nobes and L. Radom, University of Georgia, Athens, USA 11 List of Participants Dr. A. Alex Dr. J. R. Alvarez-Idaboy Dr. J. L. Andres Mr.X.Assfeld Prof. V. Aviyente Prof. R.D. Bach Prof. T. Bally Prof. M. I. Ban Mr. T. Barlow Mr. J. A. Barnes Prof. H. Basch Dr. M. J. Bearpark Dr. U. Berg Prof. F Bernardi Prof. J. Bertran Dr. R. G. A. Bone Dr. B. Brocklehurst Miss C. Burgess Prof. L. Butler Dr. D. Buttar Dr. C. Canepa Prof. M. F. Chanon Prof. M. S. Child Ms. S. Chiu Dr. T. Clark Mr. S. Clifford Dr. D. L. Cooper Mr. T. P. Cunningham Mr. M. Davidson Dr. V. Dillet Dr. G. Domotor Mr. A. H. Elcock Miss J. Fidler Dr. I. Fleming Prof. M. M. Franc1 Prof, B. Fuchs Prof. R. Gallo Prof. R. Gandolfi Dr. J. Gerratt Dr. G. H. Grant Dr. M. Hand Dr. D. M. Hirst Mr. M. Hofmann Prof. K. N. Houk Dr. K. Ishii Prof. W. L. Jorgensen Dr.P. B. Karadakov Prof. M. Karplus Prof. H. F. Koch Prof. T-S.Lee Mrs. L. Linney Prof. K. Mackenzie Mr. C. Maerker Mr. N. 0.J. Malcolm Dr. J. J. W. McDouall Prof. J. Michl Prof. R. Minyaev Dr. P. C. H. Mitchell Mr. V. Moliner Mr. A. Mulholland Prof. E. Nakamura Ms. N. Nendel Dr. M. T. Nguyen Dr. G. Nyman Dr. M. Olivucci Mr. I. J. Palmer Pjzer Central Research, Sandwich, UK Uppsala University, Sweden University of Girona, Spain UA 510 CNRS, Nancy I, France Bogazici University, Istanbul, Turkey Wayne State University, Detroit, USA University of Friborg, Switzerland JATE University of Szeged, Hungary University of Oxford, UK University of Bath, UK Bar-Ilan University, Ramat Gan, Israel King’s College, London, UK University ofLund, Sweden University of Bologna, Italy University of Barcelona, Spain Molecular Research Institute, California, USA University of Shefield, UK University College, Dublin, Eire University of Chicago, Illinois, USA University of Bath, UK University of Turin, Italy Faculti Sciences, Marseille, France University of Oxford, UK University of Manchester, UK University of Erlangen-Nurnberg, Germany King’s College, London, UK University of Liverpool, UK University of Liverpool, UK University of Manchester, UK Laboratoire de Chimie Theorique, Nancy, France JATE University of Szeged, Hungary University of Oxford, UK University of Reading, UK University of Cambridge, UK Bryn Mawr College, Philadelphia, USA Tel-Aviv University, Israel Universiti Aix-Marseille, France University of Pavia, Italy University of Bristol, UK University College Dublin, Eire University of Bath, UK University of Warwick, UK University of Erlangen-Nurnberg, Germany University of California, Los Angeles, USA Yokohama, Japan Yale University, New Haven, USA University of Bristol, UK Harvard University, Cambridge, USA Ithaca College, New York, USA National Chung Hsing University, Taiwan University of Bath, UK University of Bristol, UK University of Erlangen-Nurnberg, Germany University of Manchester, UK University of Manchester, UK University of Colorado, Boulder, USA Rostov University, Russia University of Reading, UK Universitat Jaume I, Spain University of Oxford, UK Tokyo Institute of Technology, Japan Georgia Institute of Technology, USA University of Leuven, Belgium University of Cambridge, UK University of Bologna, Italy University of Manchester, UK iii Prof.P. Paneth Dr. W. Quapp Prof. A. Rastelli Dr. C. A. Reynolds Dr. G. Richards Dr. C. Richardson Prof. J. H. Ridd Prof. M. A. Robb Dr. S. H. Robertson Mr. A. Robinson Dr. M. A. Rodriguez Mr. V. S. Safont Dr. J. P. B. Sandal1 Dr. P. J. Sarre Dr. M. Saunders Prof. W. Saunders Prof. H. B. Schlegel Prof. P. von R. Schleyer Mr. P. Schreiner Dr. G. Sexton Prof. S. Shaik Prof. J. P. Simons Mr. B. R. Smith Dr. M. Sola i Puig Dr. L. L. Stacho Dr. A. J. Stone Dr. M-D. Su Prof.W. T. Borden Mr. T. Thorsteinsson Prof. J. Tomasi Prof. G. Tonachini Prof. D. G. Truhlar Mr. I. Tunon Dr. J. E. Upham Mr. G. Vacek Dr. P. Th. van Duijnen Miss A. van Keer Mr. H. Vansweevelt Dr. T. Vernali Dr. A. Venturini Prof. D. C. Walker Dr. R. A. Walsh Ms. G. Waschewsky Mr. M. B. Weaver Dr. 0.Wiest Prof. F. Williams Dr. I. H. Williams Miss S. Wilsey Mr. C. Wilson Dr. S. A. Wilson Miss N. Yamamoto Dr. R. Zwaans Technical University of Lodz, Poland University of Leipzig, Germany University of Modena, Italy University ofEssex, UK University of Oxford, UK Smithkline Beecham, Betchworth, UK University College, London, UK King’s College London, UK University of Leeds, UK University of Oxford, UK University ofLa Rioja, Logrono, Spain Universitat Jaume I, Spain University of Exeter, UK ScientiJic Editor, Faraday, University ofNottingham, UK Smithkline Beecham, Welwyn, UK University of Rochester, New York, USA Wayne State University, Detroit, USA University of Erlangen-Nurnberg, Germany University of Georgia, Athens, USA Zeneca Agrochemicals, Bracknell, UK Hebrew University, Jerusalem, Israel University of Oxford, UK King’s College London, UK University of Girona, Spain JATE University of Szeged, Hungary University of Cambridge, UK King’s College London, UK University of Washington, Seattle, USA University of Liverpool, UK University of Pisa, Italy University of Turin, Italy University of Minnesota, Minneapolis, USA University of Valencia, Spain University of Reading, UK University of Georgia, Athens, USA University of Groningen, The Netherlands University of Leuven, Belgium University of Leuven, Belgium Bogazici University, Istanbul, Turkey I.Co.CEA-CN R, Bologna, Italy University ofBritish Columbia, Vancouver, Canada University of Reading, UK University of Chicago, Illinois, USA ICI Materials, Wilton Research Centre, UK University of California, Los Angeles, USA University of Tennessee, Knoxville, USA University of Bath, UK King’s College London, UK University of Warwick, UK Rutherford Appleton Laboratory, Didcot, UK King’s College London, UK University of St Andrews, UK iv Index of Contributors* Andres, J., 1703 Mitchell, P.C. H., 1606, 1802 Assfeld, X., 1743 Moliner, V., 1703, 1735, 1737, 1738 Balaji, V., 1653 Morokuma, K., 1789 Bally, T., 1615, 1674, 1733, 1808 Myers, T. L., 1581 Ban, M. I. 1610 Nakamura, E., 1614,1789,1810 Barnes, J. A., 1709 Nakamura, M., 1789 Barker, S. A., 1689 Nguyen, M. T., 1610,1616,1669,1733, Beno, B., 1599 1734,1739,1771,1800,1807 Bernardi, F., 1617, 1669, 1671, 1672 Nyman, G., 1743 Bertran, J., 1679,1757, 1800, 1806 Olivucci, M., 1613,1617, 1670, 1744 Blake, J. F., 1727 Paneth, P., 1737,1738 Borden, W. T., 1606,1614,1616, 1671, Plitt, H. S., 1653 1673,1675,1689,1733,1734,1735, Quapp, W., 1609 1743,1744,1802,1807 Raimondi, L., 1599 Bottoni, A., 1617 Raimondi, M., 1643 Butler, L. J., 1581, 1612, 1613, 1614, Rauhut, G., 1783 1671,1677,1809 Raymond, M.K., 1653 Child, M. S., 1739 Reddy, A. C., 1631 Chiu, S. S-L., 1575 Reynolds, C. A., 1605,1744 Clark, T., 1669,1678,1783, 1807,1808, Robb, M. A., 1617,1672 1809,1810 Rodriguez, M. A., 1738 Coitino, E. L., 1745 Safont, V. S., 1703 Cooper, D. L., 1643 Saunders, W., 1735,1738,1809 Craig, S. L., 1663 Schlegel, H. B., 1569,1609,1610,1611 Cramer, C. J., 1802 Schleyer, P. von R., 1559, 1605, 1606, Dejaegere, A., 1763 1671,1673,1674,1677,1680,1734, Downing, J. W., 1653 1743,1744,1801,1805 Francl, M. M., 1605,1740,1744 Severance, D. L., 1727 Gerratt, J., 1643, 1672, 1673, 1801 Shaik, S., 1605, 1606, 1610, 1612, 1615, Getty, S. J., 1689 1631,1669,1670,1671,1673,1674, Hawkins, C. D., 1802 1675,1677,1679,1734,1738,1800, Hillier, I.H., 1575 1806,1808,1809 Houk, K. N., 1599,1605,1614,1615, Silla, E., 1757 1616,1672,1678,1680,1810 Simons, J. P., 1613 Hrovat, D. A., 1689 Stacho, L. L., 1609,1611 Hu, W-P., 1715 Stone, A. J., 1610,1663,1673,1678, Jiao, H., 1559 1679,1680 Jorgenson, W. L., 1727,1735, 1743,1744 Storer, J., 1599 Karadakov, P. B., 1643,1672,1673, Tomasi, J., 1610, 1616, 1679, 1745, 1799, 1799 1800,1801,1805,1806,1808,1810 Karplus, M., 1609, 1611,1612,1674, Truhlar, D. G., 1608,1611,1614,1670, 1680,1744,1763,1800,1802,1804, 1679,1715,1735,1740,1743,1801, 1806,1809 1802,1804,1806 Kash, P. W., 1581 Tuiion, I., 1757 Kitchen, D. C., 1581 van Duijnen, P. Th., 1611,1612,1805 Koga, N., 1789 Vanquickenborne, L. G., 1771 Landuyt, L., 1771 Ventura, 0.N., 1745 Li, Y., 1599 Venturini, A., 1617 Liang, X.,1763 Waschewsky, G.C. G., 1581 Lim, D., 1727 Walsh, R. A., 1615,1616,1678,1807 Liu, Y-P., 1715, 1735 Williams, F., 1605,1681, 1733, 1810 Mackenzie, K., 1810 Williams, I. H., 1615, 1673, 1679, 1709, Maerker, C., 1799 1737,1738,1739,1740,1799 McDouall, J. J. W., 1575, 1610 Wilkie, J., 1709 Michl, J., 1606, 1653, 1675, 1677, 1678, Wilson, S. A., 1616, 1674, 1680 1680,1733,1809 Xu, J. D., 1689 * The page numbers in heavy type indicate papers submitted for discussion. Cumulative Author Index 1994 Aas, N., 1015 Borge, G., 1227 Craig, S.L., 1663 Gill, D. S., 579, 583 Iwasaki, K., 121 Abbott, A. P., 1533 Boriscnko, V. N., 109 Cramer, C. J., 1802 Gill, J. B., 315 Jacobs, W.P. J. H., 1191Afanasiev, P., 193 Bottoni, A., 1617 Crawford, M. J., 817 Goede, S.J., 327, 1363 Jakubov, T., 783 Agren, H., 1479 Boutonnet-Kizling, M., Cruzeiro-Hansson, L., 1415 Gomez, C. M., 339 Jameel, A. T., 625 Aikawa, M., 911 1023 Cullis, P. M., 727 Gonpalves da Silva, A. M., Janchen, J., 1033 Aitken, C. G., 935 Bowker, M., 1015 Curtis, J. M., 239 649 Jayakumar, R., 161 Akanuma, K., 1171 Bozon-Verduraz, F., 653 D'Alagni, M., 1523 Goodfellow, J. M., 1415 Jayasooriya, U.A., 1265 Akolekar, D. B., 1041 Bradley, C. D., 239 Dan& N-T., 875 Gouder, T. H., 1285 Jenneskens, L. W., 327,Albcry, W. J., 1115 Bradshaw, A. M., 403 Danil de Namor, A. F., 845 Goworek, T., 1501 1363 A1daz.A.. 609 Braun, B. M., 849 Das, T. N., 963 Gray, P. G., 369 Jennings, B.J., 55 Alfimov, M. V., 109 Brcysse, M., 193 Dasannacharya, B. A,, 1149 Green, W. A., 83 Jiang, D-z., 1351 Al-Ghefaili, K. M., 383,1047 Briggs, B., 727 Davey, R. J., 1003 Grein, F., 683 Jiang, P-Y., 591 Ah, V., 579, 583 Brocklehurst, B., 271 Davidson, K., 879 Grieser, F., 1251 Jiang, P. Y., 93 Aliev, A. E., 1323 Brogan, M. S., 1461 DeBenedetto, G. E., 1495 Grifith, W. P., 1105 Jiao, H., I559 Allegrini, P., 333 Brown, N. M. D., 1357 Defrancc, A., 1473 Grimshaw, J., 75 Jobic, H., 1191 Allen, N.S., 83 Brown, R. G., 59 Dejaegere, A., 1763 Grzybowska, B., 895 Johansson, L. B.-A., 305 A1 Rawi, J. M. A., 843 Brown, S.E., 739 Demeter, A,, 411 Guelton, M., 895 Johari, G. P., 883, 1143 Amorim da Costa, A. M., 689 Bruna, P. J., 683 Dcmpscy, P., 1003 Guilhaume, N., 1541 John, S.A,, 1241 Amoskov, V. M., 889 Brzczinski, B., 843,1095 Demri, D., 501 Guillaume, F., 1313 Jorgensen, W. L., 1727,Ando, M., 1011 Buckley, A. M., 1003 Derrick, P. J., 239 Guldi, D. M., 1391 1735,1743, 1744 AndrCs, J., 1703 Buemi, G., 1211 DewingJ., 1047 Gulliya, K. S., 953 Joseph, E. M., 387 Andrews, S.J., 1003 Burdisso, M., 1077 Diagne, C., 501 Hachey, M., 683 Joshi, P. N., 387 Anson, C. E., 1449 Busca, G., 1161,1293 Dickinson, E., 173 Haeberlein, M., 263 Jurs, P. C., 1553 Aragno, A., 787 Buschmann, H-J., 1507 Dines, T. J., 1461 Hall, D. I., 517 Kagawa, S., 349 Arai, S., 1307 Butler, L. J., 1581, 1612, Doblhofer, K., 745 Hall, G., 1 Kakuta, N., 1279 Aramaki, K., 321 1613,1614,1671,1677, Domen, K., 911 Hallbrucker, A,, 293 Kaler, E.W., 471 Aravindakumar, C. T., 597 1809 Dossi, C., 1335 Halpern, A., 721 Kalugin, 0.N., 297 Asai,Y., 797 Butt, M. D., 727 Doughty, A., 541 Hamnett, A., 459 Karadakov, P. B., 1643,Ashfold, M. N. R., 1357 Byatt-Smith, J. G., 493 Douglas, C. B., 471 Hancock, G., 523,1467 1672,1673,1799Asmuq K-D., 1391 Cabaleiro, M. C., 845 Downing, J. W., 1653 Handa,H., 187 Karge, H. G., 1329 Assfeld, X., 1743 Cdcercs, M., 1217 Dunmur, D. A,, 1357 Hann,K., 733 Karplus, M., 1609, 1611, Avila, V., 69 Cdccres Alonso, M., 553 Dunstan, D. E., 1261 Hao, L., 133,1223 1612,1674,1680,1774,Baba,T., 187 Cairns, J. A., 1461 Duplltre, G., 1501 Harada, S., 869 1763, 1800,1802,1804, Badia, A., 1501 Calado, J. C. G., 649 Duxbury, G., 1357 Haraoka, T., 911 1806,1809Badri, A., 1023 Caldararu, H., 213 Dwyer, J., 383, 1047 Harland, P.W., 935 Kash, P. W., 1581 Bagatti, M., 1077 Calvente, J. J., 575 Dyke, J. M., 17 Harper, R. J., 659 Kato, R., 763 Balaji, V., 1653 Calvo, E. J., 987 Eastoe,J., 487 Harriman, A., 697,953 Katsumura, Y., 93, 591 Ball, M. C., 997 Camacho, J. J., 23 Easton, C. J., 739 Harris, K. D.M., 1313, Kaur,T., 579 Ball, S.M., 523, 1467 Cameron, B. R., 935 Ebitani, K., 377 1323 Kawashima, T., 127 Bally, T., 1615, 1674, 1733, Campa, M. C., 207 Egsgaard, H., 941 Harrison, N. J., 55 Keil, M., 403 1808 Campos, A,, 339 El-Atawy, S., 879 Haruta, M., 1011 Kemball, C., 659 BBn, M. I., 1610 Canosa-Mas, C. E., 1197, El Baghdadi, A., 1313 Hashimoto, K., 1177 Kessel, D., 1073 Baonza, V. G., 553 1205 Elisei, F., 279 Hashino, T., 899 Kida, I., 103 Baonza, V.G., 1217 Capobianco, J. A., 755 Elliot, A. J., 831, 837 Hattori, H., 803 Kiennemann, A,, 501 Barbaux, Y., 895 Caraghcorgheopol, A., 213 Engbcrts, J. B. F. N., 727 Hawkins, C. D., 1802 Kim, J-H., 377 Barker, S.A., 1689 Carlile, C. J., 1149 Enomoto, N., 1279 Haymet, A. D. J., 1245 Kimura, M., 1355 Barnes, J. A., 1709 Carlsen, L., 941 Eustaquio-Rindn, R., 113 Heal, M. R., 523, 1467 King, F., 203 Barthomeuf, D., 667,675 Carvill, B. T., 233 Ewins, C., 969 Healy, T. W., 1251 Kirschner, J., 403 Basini,L., 787 Castailo, R., 1227 Fantola Lazzarini, A. L., Heenan, R. K., 487 Kita,H., 803 Bassoli, M., 363 Castro, S., 1217 423 Helmer, M., 31, 395 Kitchen, D. C., 1581 Battaglini, F., 987 Catalina, F., 83 Fausto, R., 689 Herein, D., 403 Klein, M.L., 253 Bauer, C., 517 Cataliotti, R. S., 1397 Favaro, G., 279,333 Herod, A. A., 1357 Kleshchevnikova, V.N.,Bell, A. J., 17,817 Cavasino, F. P., 311 Feliu, J. M., 609 Herrmann, J-M., 1441 629 Belton, P. S., 1099 Ceccarani, M. L., 1397 Fenn, C., 1507 Henog,B., 403 Knoche, W., 1507 Bender, B. R., 1449 Chang, T-h., 1157 Filimonov, I. N., 219,227 Heye-s, D. M., 1133 Knozinger, H., 1335 Bendig, J., 287 Charlesworth, P., 1073 Flint, C. D., 1357 Higgins, S., 459 Kobayashi, A,, 763 Bengtsson, L. A., 559 Chen, J-S., 429,717 Fogden, A., 263 Hillier, I. H., 1575 Kobayashi, H., 763 Benko, J., 855 Chen, Y-H., 617 Fornts, V., 213 Hillman, A. R., 1533 Kobayashi, T., 1011 Benniston, A. C., 953 Cheng, A., 253 Fracheboud, J-M., 1197, Hindermann, J-P., 501 Koga,N., 1789 Beno, B., 1599 Cheng, C.P., 1157 1205 Hirst, D. M., 517 Kondo, Y., 121 Bensalem, A., 653 Cherqaoui, D., 97 Franck, R., 667,675 Hiyane, I., 973 Kossanyi, J., 411 BCrcesT., 411 Chesta, C. A., 69 Francl, M. M., 1605, 1740, Hoekstra, D., 727 Kronberg, B., 1513 Bergeret, G., 773 Chevalier, S., 667, 675 1744 Hoffmann, R., 1507 Kukueva, V. V., 1479 Bernardi, F., 1617,1669, Child, M. S., 1739 Freeman, N.J., 751 Holmberg, B., 559 Kurrat, R., 587 1671,1672 Chiu, S.S-L., 1575 FrCty, R., 773 Holz, M., 849 Kusalik, P. G., 1405 Berth, J., 1679, 1757, Chmiel, G., 1153 Frey, J. G., 17, 817 Hoshino, H., 479 Kuwamoto, T., 121 1800,1806 Cho,T., 103 Frostemark, F., 559 Hosoi, K., 349 Laachir, A,, 773 Beutel, T., 1335 Christensen, P., 459 Fujiwara, Y., 1183 Houk, K.N., 1599,1605, Lajtar, L., 1153 Beyer, H. K., 1329 Clark, T., 1669,1678, 1783, Galantini, L., 1523 1614,1615,1616, 1672, Lambert, J-F., 667,675 Bickelhaupt, F., 327, 1363 1807,1808,1809,1810 Gandolfi, R., 1077 1678, 1680,1810 Lamotte, J., 1029 Biczok, L., 411 Climent, M. A., 609 Gans, P., 315 Hrovat, D. A,, 1689 Landuyt, L., 1771 Biggs, P., 1197,1205 Coates, J. H., 739 Gao,Y., 803 HSU, J-P., 1435 Langan, J. R., 75 Binet, C., 1023 CoitiAo, E. L., 1745 Garcia,R., 339 Hu, W. P., 1715 Lavalley, J-C., 1023, 1029 Black, S.N., 1003 Colmenarcs, C. A., 1285 Garcia Fierro, J-L., 1455 Hungerbiihler, H., 1391 Lnvanchy, A., 783 Blackett, P. M., 845 Coopcr, D. L., 1643 Garcia-Paileda, E., 575 Hutchings, G. J., 203 LiizBr, K., 1329 Blake, J.F., 1727 Cordischi, D., 207 Gautam, P., 697 Hutton, R. S., 345 Lazzarini, E., 423 Blanco, S., 1365 Corma,A., 213 Gavuzzo, E., 1523 Iizuka, Y., 1301, 1307 Lcaist, D. G., 133, 1223 Blandamer, M. J., 727 Cormier, G., 755 Geantet, C., 193 Ikawa, S-i., 103 Lee, J., 1553 Blower, C., 919,931 Corradini, F., 859, 1089 Gengembre, L., 895 Ikonnikov, I. A., 219 Lcgon, A. C., 1365 Bochenl, P., 1473 Corrales, T., 83 Gerratt, J., 1643, 1672, Ilayszyn, M., 1411 Lci,G-D., 233 Boddenbcra. B.. 1345 Cosa, J. J., 69 1673,1801 Indovina, V., 207 Lcrner, B. A., 233 '17Boggis, S.i:, Costas, M., 1513 Getty, S.J., 1689 Inoue, Y., 797,815 Leslie, M., 641 Borden, W.T., 1606, 1614, Cottier, D., 1003 Giglio, E., 1523 Ishiga, F., 979 Li, J., 39 1616,1671,1673,1675, Coudurier, G., 193 Gil, A.M., 1099 Ishigure, K., 93, 591 Li, P., 605 1689,1733,1734,1735, Courcot, D., 895 Gil, F. P. S. C., 689 Isoda, T., 869 Li, X., 1429 1743,1744,1802,1807 Cracknell, R.F., 1487 Gilchrist, J., 1149 Ito,O., 571 Li, Y., 947,1599 vi Liang, X., 1763 Morikawa, A., 377 Primet, M., 1541 Shihara, Y., 549 Ugo, R., 1335 Liang, Y., 1271 Morioka, Y., 1279 Pringle, T. J., 1015 Shiralkar, V. P., 387 Umemoto, H., 549 Lillerud, K. P., 1547 Morokuma, K., 1789 Priyadarsini, K. I., 963 Shishido, T., 803 Unayama, S-i., 549 Lim,D., 1727 Morokuma, M., 377 Pryamitsyn, V. A., 889 Shizuka, H., 533 Upadhyaya, H. P., 825 Lin, J., 355 Momson, C. A., 755 Psaro, R., 1335 Siders, P., 973 Valat, P., 411 Lincoln, S. F., 739 Mount, A. R., 1115,1121 Quapp,W., 1609 Silla, E., 1757 Valls, M.J., 609 Lindblom, G., 305 Muir, A. V. G., 459 Rabold, A., 843 Silva, C. J., 143 van Duijnen, P. Th., 1611, Liu, B-T., 1435 Mukhejee, T., 711 Raimondi, L., 1599 Silva, F., 143 1612,1805 Liu,C-W., 39 Mukhopadhyay, R., 1149 Raimondi, M., 1643 Silveston, R., 1513 van Hooff, J. H. C., 1033 Liu,X., 249 Myers, T. L., 1581 Ramaraj, R., 1241 Simkiss, K., 641 Vanquickenborne, L. G., Liu, Y-P., 1715,1735 Nagaishi, R., 93, 591 Rama Rao, K.V. S., 825 Simons, J. P., 1613 1771 Sims, I. R., 1473 van Santen, R. A., 1191Loginov, A. Yu., 219,227 Nagaoka, H., 349 Ramis, G., 1293 Lohse, U., 1033 Naito, S., 899, 1355 Ramsden, J. J., 587 Singh, J., 579, 583 van Wolput, J. H. M. C., Long, A., 1547 Naito, T., 763 Rao, B. S. M., 597 Singh, R., 583 1033 Longdon, P.J., 315 Nakamura, E., 1614,1789, Rastelli, A., 1077 Smart, S. P., 1313 Varandas, A. J. C., 1381 Lorenzelli, V., 1293 1810 Rauhut, G., 1783 Smith, I. W. M., 1473 Vedrine, J. C., 193 Venanzi, M., 435Loveday, D. C.,, 1533 Nakamura, M., 1789 Raymond, M. K., 1653 Smith, K. M., 1073 Lu, J-X., 39 Nalewajski, R. F., 1381 Reddy, A. C., 1631 Smith, T. D., 919,931 Ventura, 0.N., 1745 Lunelli, B., 137 Navaratnam, S., 83 Rehani, S. K., 583 Soares, V. A. M., 649 Venturini, A., 1617 Ma, J., 1351 Neoh, K. G., 355 Rettig, W., 59 Sokolowski, S., 1153 Vigue, J., 1553 Mabuchi, M., 899 Nerukh, D. A., 297 Rey,F., 213 Soria, V., 339 Villamagna, F., 47 Machado, V. G., 865 Nguyen, M. T., 1610,1616, Reynolds, C. A., 1605, 1744 Spiro, M., 617, 1105 Villemin, D., 97 Mackenzie, K., 1810 1669,1733,1734,1739, Rezende, M.C., 865 Stachb, L. L., 1609, 1611 Visscher, P. B., 1133 Rhodes, N. P., 809 Stanley, D. R., 1003 Vlietstra, E. J., 327, 1363 Mackie, J. C., 541 1771,1800,1807 Mackintosh, J. G., 1121 Nicholson, D., 181, 1487 Ricchiardi, G., 1161 Stewart, B., 969 Vollarov& O., 855 Macpherson, A. N., 1065 Nickel, U., 617 Richter, R., 17 Stoeckli, F., 783 Vollmer, F., 59 Madariaga, J. M., 1227 Ninomiya, J., 103 Robb, M. A., 1617,1672 Stone, A. J., 1610,1663, Volt& J-C., 1161, 1441 Maeda,T., 899 Nishihara, H., 321 Robertson, E. G., 1055 1673,1678,1679,1680 von Rague Schleyer, P., 1559Maerker, C., 1799 Nogami, T., 763 Rocha, M., 143 Storer, J., 1599 Maestre, A., 575 Nonaka, O., 121 Rochester, C.H., 203 Sueiras, J-E., 1455 Vyunnik, 1. N., 297 Maginn, S. J., 1003 Norton, J. R., 1449 Rodes, A., 609 Sun, L. M., 369 Wales, D. J., 1061 Maher, J., 1553 Nuiiez, J., 1217 Rodriguez, M. A., 1738 Sun,T., 1351 Walsh, R. A., 1615, 1616, Mahy, J. W. G., 327,1363 Nuiiez Delgado, J., 553 Rofia, S., 137 Suquet, H., 667,675 1678,1807 Maity, D. K., 703 Nyholm, L., 149 Rosenholm, J. B., 733 Surov, Y. N., 297 Wang, C. F., 605 Wang, J., 1245Makarova, M. A., 383, Nyman, G., 1743 Rosmus, P., 517 Suzuki, T., 549 1047 Occhiuzzi, M., 207,905 Rosseinsky,D. R., 1127 Svishchev, I. M., 1405 Waschewsky, G. C. G., 1581 Rossi, P. F., 363 Szostak, R., 1547 Watanabe, H., 571Maksymiuk, K., 745 Ohji, N., 1279 Malatesta, V., 333 Ohtsu, K., 127 Rout, J. E., 1003 Tabata, M., 1171 Waters, M., 727 Tabrizchi, M., 17 Wayne, R.P., 1197, 1205 Malcolm, B. R., 493 Okamura, A., 803 Rouvet, F., 1441 Malitesta, C., 1495 Olazabal, M. A., 1227 Rowe, B. R., 1473 Tagliazucchi, M., 859, 1089 Weckstrom, K., 733 Mallon, D., 83 Olejnik, J., 1095 Rudham, R., 809 Takagi, T., 121 Weingartner, H., 849 Mandal, A. B., 161 Oliveri, G., 363 Ryde,N., 167 Takahashi, K., 155 Weir, D. J., 751 Marcheselli, L., 859 Olivucci, M., 1613, 1617, Sacco,A., 849 Takasawa, A., 911 Werner, H., 403 Marchetti, A., 859, 1089 1670,1744 Sachtler, W. M. H., 233, Takenake, S., 1537 Whitaker, B. J., 1 Mariani, M., 423 Onishi, T., 911 1335 Tamaura, Y., 1171 White, L. R., 1251 Safont, V. S., 1703 Tamura, K-i., 533 Whitehead, M. A., 47Martins, A., 143 Ono,Y., 187 Saitoh, T., 479 Tanaka,I., 349 Wikander, G., 305Maruya, K-i., 911 Oradd, G., 305 Salagre, P., 1455 Tanigaki, H., 1307 Wilde, C.P., 1233Masetti, F., 333 Ortica, F., 279 Mason, R. S., 1373 Oswal, S. L., 1083 Salmon, G. A., 75 Taravillo, M., 1217 Wilhelm, M., 1391 Sam, D. S. H., 1161 Tassi, L., 859, 1089 Wilkie, J., 1709Massucci, M., 445 Ota, K-i., 155 MatijeviC, E., 167 Otlejkina, E. G., 297 Sanada, M., 1307 Tateno, A., 763 Williams, D. E., 345 Tatham, A., 1099 Williams, F., 1605, 1681, Matsuda, J., 321 Otsuka, K., 451 Sano, T., 869 1733, 1810 Matsumura, Y., 1177 Ottavi, G., 333 Sapre, A. V., 825 Taylor, A., 1003 May, I. P., 751 Ouellette, D. C., 837 Sarre, P. J., 517 Taylor, M. G., 641 Williams, 1. H., 1615, 1673, Sassi, P., 1397 Teixeira-Dias, J.J. C., 689 1679,1709,1737, 1738, Mazzucato, U., 333 Owari,T., 979 Teo, W. K., 355 1739, 1740, 1799 McDouall, J. J. W., 1575, Ozutsumi, K., 127 Sato, K., 797 1610 Padley, M. B., 203 Saunders, W., 1735, 1738, Teramoto, M., 979 Wilpert, A., 287 Teraoka, Y., 349 Wilson, S. A., 1616, 1674, McGilvery, D., 1055 Pais, A. A. C. C., 1381 1809 Saur, O., 1029 Thompson, K. M., 1105 1680Mchedlov-Petrossyan, N. O., Pal, H., 711 629 Pal-Borbkly, G., 1329 Sbriziolo, C., 311 Thompson, N. E., 1047 Wintgens, V., 411 McKay, H. A. C., 1553 Palleschi, A., 435 Scaramuzza, L., 1523 Thorn, J. C., 1365 Woermann, D., 875 McNaughton, D., 1055 Paneth, P., 1737,1738 Schedel-Niedrig, Th., 403 Timms, A. W., 83 Wohlers, M., 403 Meadows, G., 1429 Paradisi, C., 137 Schlegel, H. B.,.1569, 1609, Timney, J. A., 459 Wolthuizen, J. P., 1033 1610,1611 Togawa, T., 1171 Wormald, C. J., 445Medforth, C. J., 1073 Pardo,A., 23 Medina, F., 1455 Parry, A. J., 1373 Schleyer, P. von R., 1559, Tomasi, J., 1610, 1616, Xin,Q., 973 Melrose, J. R., 1133 Parsons, B. J., 83 1605, 1606,1671,1673, 1679,1745,1799,1800, Xu, J. D., 1689 Merga,G., 597 Patel, S. G., 1083 1674,1677,1680,1734, 1801,1805, 1806, 1808; Yagci, Y., 287 Meunier, F., 369 Pathmanathan, K., 1143 1743,1744,1801,1805 1810 Yamaji, M., 533 Mezyk, S. P., 831 Patrykiejew, A., 1153 Schlogl, R., 403 Tosi, G., 859, 1089 Yamamoto, M., 899,1355 Michl, J., 1606, 1653, 1675, Paul, D. K., 1271 Schnabel, W., 287 Touret, O., 773 Yamanaka, I., 451 1677, 1678, 1680,1733, Pavanaja, U.B., 825 Scremin, M., 865 Tournayan, L., 773 Yamasaki, M., 869 1809 Pedulli, G.F., 137 Seddon, B. J., 605 Trau, M., 1251 Yamasu, H., 1537 Mills, A., 1429 Peters, M. P. J., 1033 Seidel, A., 1345 Travers, D., 1473 Yamauchi, N., 1307 Milton, D. M. P., 1373 Penfold, J., 1553 Sellen, D. B., 1357 Trejo, A., 113 Yanes, C., 575 Min, E-z., 1351 Pen& W., 605 Severance, D. L., 1727 Treviiio, H., 1335 Yang, Z-Q., 947 Shahid, G., 507,513 Truhlar, D. G., 1608, 1611, Yano,H., 869Minaev, B. F., 1479 Pepe,F., 905 Misono, M., 1183 Pereira, C. M., 143 Shaik, S., 1605, 1606, 1610, 1614,1670,1679,1715, Yasuda, H., 1183 1612,1615,1631,1669, 1735,1740,1743,1801, Yeh, C-t., 1157Mitchell, P. C. H., 1606, PCrez, J. M., 609 1802 Perrichon, V., 773 1670,1671,1673,1674, 1802,1804,1806 Yoshitake, H., 155 1675,1677,1679,1734, Truscott, T.G., 1065,1073 Yotsuyanagi, T., 93,479Mitchell, P. J., 1133 Peter, L. M., 149 1738,1800,1806,1808, Tsuchiyama, T., 1355 Young, R. N., 271Mittal, J. P., 597,703, 711, Petrov, N. Kh., 109 825 Pispisa, B., 435 1809 Tsuji, H., 803 Zambonin, C. G., 1495 Miyake, Y., 979 Pivnenko, N. S., 297 Shallcross, D. E., 1197, Tsuji, M., 1171 Zanotto, S. P., 865 Mizuno, N., 1183 Plane, J. M. C., 31,395 1205 Tsunashima, S., 549 Zhang, M., 1233 Mizushima, T., 1279 Plitt, H. S., 1653 Sharma,A., 625 Tsunetoshi, J., 1307 Zhang,X., 605 Moffat, J. B., 1177 Plowman, R., 1003 Shaw, N., 17,817 Tung, C-H., 947 Zhang, Z. C., 1335 Sheil, M. M., 239 Tuiibn, I., 1757 Zholobenko, V.L., 233,Mohan, H., 597,703 Porcar, I., 339 Moliner, V., 1703, 1735, Potter, C. A. S., 59 Shen, J-p., 1351 Turco Liveri, M. L., 311 1047 1737,1738 Powell, D. B., 1449 Sheppard, N., 507,s 13, Turco Liveri, V., 311 Zhong, G. M., 369 Monk, P. M. S., 1127 Poyato, J. M. L., 23 1449 Turner, P. H., 1065 Ziolek, M., 1029 Mordi, R. C., 1323 Prenosil, J. E., 587 Sherwood, P. M. A., 1271 Udagawa, T., 763 Zubarev, V. E., 721 Moriguichi, I., 349 Previtali, C. M., 69 Shiao, J-C., 429 Ueno, A., 1279 Zundel, G., 843,1095 vii The following papers were accepted for publication between 1st and 30th April 1994: Determination of the transfer thermodynamic functions for the zinc(II), cadmium(Ir), mercury(I1) and mercury(1) ions from water to methanol, dimethyl sulfoxide, acetonitrile, pyridine and N,N-dimethylthioformamideand of standard electrode potentials of the M2+/M(s)couples in these solvents I.Persson, M. Chaudry, K. C. Dash, E. Kamienska-Piotrowicz and Y. Kinjo Transfer thermodynamic study on the copper(I1) ion from water to methanol, acetonitrile, dimethyl sulfoxide, pyridine and tetrahydrothiophene I. Persson and M. Chaudhry Determination of the transfer thermodynamic functions for some monovalent ions from water to N,N-dimethylthioformamide, and for some anions from water to methanol, dimethyl sulfoxide, acetonitrile and pyridine, and standard electrode potentials of some M+N(s) couples in N,N-dimethylthioformamideI. Persson, D. Inerowicz and W. Li Photoluminescence spectra resulting from hydroxy groups on magnesium oxide supported on silica H.Yoshida, T. Tanaka, T. Funabiki and S. Yoshida Ligand exchanges between ethanol and some amines in excited mercury complexes S. Yamamoto, T. Nagaoka, Y.Sueishi and N. Nishimura Crossover behaviour and critical amplitude of the viscosity of binary liquid mixtures of critical composition D. Woermann and A. Zielesny Enzyme catalysis and transition structures in vacuo. Transition structures for the enolization, carboxylation and oxygenation reactions in ribulose- 1,5bisphosphate carboxylate/oxygenase enzyme (Rubisco) 0. Tapia, J. Andres and V. S. Safont Microcalorimetric titration of a-cyclodextrin with some straight-chain a,w-dicarboxylates in aqueous solution at different temperatures D.Hallen, I. Gomez-Orellana and M. Stodeman Atmospheric lifetime, its application, and its determination: CFC-substitutes as a case study A. R. Ravishankra and E. R.Lovejoy Determination of aggregate structures by combined light-scattering and rheological studies S. D. T. Axford and T. M. Herrington AlP0,-Al,O, catalysts with low alumina content. IV. Effect of fluoride ion addition on texture, surface acidity and catalytic performance in cyclohexane and cumene conversions J. M. Campelo, A. Garcia, D. Luna, J. M. Marinas, A. A. Romero, J. A. Navio and M. Macias Structure and transport in concentrated micellar solutions with a lower consolute boundary G. G. Warr, J. M. Keller and H.D. Ludemann Characterisation of carbon-supported ruthenium-tin catalysts by high-resolution electron microscopy S.Galvagno, G. Neri, R. Pietropaolo and J. Schwank Synthesis of SAPO-34: High silicon incorporation in the presence of morpholine as template A. M. Prakash and S. Unnikrishnan Conductivity and dielectric relaxation in hydrated fused salts G. P. Johari, D. A. Wasylyshyn and S. K. Jain Photoelectrochemistry using quinone radical anions B. R. Eggins and P.K. J. Robertson Surface distribution and heteroatom removal activity of equilibrium adsorption prepared, doubly promoted (Zn, Co)Mo/Al,O, catalysts A. L. Agudo, J. L. G. Fierro, H. J. Thomas, C. V. Caceres and M. Blanco Reactivity of zeolite hydroxy groups toward 0-donor bases. H-D exchange with 3-methylpentane C. J. A. Mota, R.L. Martins, L. Nogueira and W. B.Kover Selective oxidative coupling of methane catalyzed over hydroxyapatite ion-exchanged with lead J. B. Moffat, Y. Matsumura, S. Sugiyama, H. Hayashi, N. Shigemoto and K. Saitoh Water distillation through PTFE hydrophobic membranes in a stirred cell M. Vazquez-Gonzalez and L. Martinez The effect of preferential solvation on Gibbs energies of ionic transfer D. J. Schiffrin, A-K. Kontturi, K. Konturri and L. Murtomaki viii Hydroxylaminewater: Intermolecular potential function and simulation of hydrated NH20H B. M. Rode, S. Vizoso and M. G. Heinzle Some thermodynamic properties of aqueous amino acid systems at 288.15,298.15,313.15, and 328.15 K: Group additivity analyses of standard-state volumes and heat capacities A. W. Hakin, M.M. Duke, J. L. Marty and K. E. Preuss Direct observation of native and unfolded glucose oxidase structures by scanning tunnelling microscope E. Wang, Q. Chi, J. Zhang and S. Dong Influence of immobilising anions on the redox switching of polyaniline M. Kalaji, V. W. Jones, G. Walker, C. Barbero and R. Kotz Electronic states and the metal-insulator transition in caesium-ammonia solutions M. L. Klein, Z. Deng and G. J. Martyna Direct observation of aluminium guest-ions in the silicate phases of cement minerals by 27Al MAS NMFt spectroscopy C. Hall, J. Skibsted and H. J. Jakobsen Preparation and characterization of multiple ion-exchanged PVTiO, catalysts J-M. Tatibouet, K. Hadjivanov, J. Lamotte, J-C. Lavalley, J. Saint-Just and M. Che Formation of two-dimensional structures from colloidal particles on fluorinated oil substrate P. A.Kralchevsky, G. S. Lazarov, N. D. Denkov, 0. D. Velev and K. Nagayama Fractal properties of a homologous series of structures S. El-Basil Pd(1) location and adsorbate interactions in PdH-SAPO-34 studied by EPR and electron spin-echo modulation spectroscopies L. Kevan, G-H. Back, J-S. Yu and V. Kurshev The structure of the diamminecopper(1) ion in solution. An X-ray absorption spectroscopic study D. G. Nicholson, A. Moen and G. Lamble Does mass action law breakdown occur in small thermodynamic systems? A. V. Sokirko Physicochemical and catalytic properties of polyaniline protonated with 12-molybdosphosphoric acid M. Hasik, J. Pozniczek, Z. Piwowarska, K.Kruczala, R. Dziembaj, A. Bielanski and A. Pron Kinetic study in a microwave-induced plasma afterglow of the Cu (42S) atom reaction with N20 from 458-980 K and with NO, from 303-762 K C. Vinckier, T. Verhaeghe and I. Vanhees Microwave spectrum and rotational isomerism of gaseous nitrosoethane, CH,CH,NO A. P. Cox, J. A. Hardy, J. Randell, H. W. Kroto, M. Maier and D. R. Milverton The formation and structure of mono-and di-bismuth hydroxide and fluoride complexes in molten NH,NO,.l SH20 at 50 "C B. Holmberg, F. Frostemark and L. Bengtsson Study of the conformational equilbrium of 1 -chlorobutane by free-jets and conventional microwave spectroscopy W. Caminati, S. Melandri, P. G. Favero, D. Damiani and L. B. Favero Underpotential deposition and dielectric electronegativity scale C.Alcober, S. A. Bilmes, E.J. Calvo and D. Posadas The colourful world of complex-forming bimolecular reactions J. Troe NMR determination of EPR hyperfine coupling constants of some 5-(n-alkyl)- 1,133- tetrakis(trideuteriomethyl)isodolin-2-yloxyls D. G. GilIies, L. H. Sutcliffe and X.Wu ix FARADAY DIVISION INFORMAL AND GROUP MEETINGS Statistical Mechanics and Thermodynamics Group Cellular Automata and their Applications to Molecular Fluids To be held at the University of Manchester on 19 and 20 July 1994 Further information from Dr A. Masters, Department of Chemistry, University of Manchester, Manchester M13 9PL Division Autumn Meeting: Reactions and Mechanisms for Fine Chemicals To be held at the University of Glasgow on 6-9 September 1994 Further information from Dr J.F. Gibson, The Royal Society of Chemistry, Burlington House, London W1V OBN ~ Gas Kinetics Group 13th International Symposium on Gas Kinetics To be held at University College, Dublin on 11-15 September 1994 Further information from Dr H. Sidebottom, Department of Chemistry, University College, Dublin Electrochemistry Group with the SCI ELECTROCHEM 94 To be held in Edinburgh on 12-16 September 1994 Further information from Professor D. E. Williams, Department of Chemistry, University College London, 20 Gordon Street, London WClH OM Biophysical Chemistry Group with the Industrial Division Biotechnology Group Peptide + Water = Protein To be held at University College, London on 19 September 1994 Further information from Professor J.L. Finney, Department of Physics and Astronomy, University College London, Gower Street, London WClE 6BT British Carbon Group Applications of Microporous Carbons To be held at the University of Leeds on 28 and 29 September 1994 Further information from Professor B. Rand, Department of Chemistry, The University, beds LS2 9JT Theoretical Chemistry Group with CCPl Electronic Structure: From Molecules to Enzymes To be held at University College London on 30 November 1994 Further information from Dr P. J. Knowles, School of Chemistry, University of Sussex, Falmer, Brighton BN1 9QJ Division Annual Congress: Lasers in Chemistry To be held at Heriot Watt University, Edinburgh on 1&13 April 1995 Further information from Dr J.F. Gibson, The Royal Society of Chemistry, Burlington House, London W1V OBN Division Joint Meeting with the Division de Chimie Physique de la Societe' Francaise de Chimie, Deutsche Bunsen Gesellschaft fur Physikalische Chemie and Associazione Italiana di Chimica Fisica Fast Elementary Processes in Molecular Systems To be held at the Universite De Lille, France on 16-30 June 1995 Further information from Dr C. Troyanowsky, Division de Chimie Physique, Laboratoire de Chimie Physique, 11 rue Pierre et Marie Curie, 75005 Paris, France British Carbon Group Carbon '96 To be held at the University of Newcastle upon Tyne on 7-12 July 1996 Further information from Dr K. M. Thomas, Northern Carson Research Laboratories, The University, Newcastle upon Tyne NE1 7RU X THE ROYAL SOCIETY OF CHEMISTRY, FARADAY DIVISION, GENERAL DISCUSSION 98 Polymers at Surfaces and Interfaces University of Bristol, 12-14 September 1994 Organising Committee: Professor Sir Sam Edwards (Chairman) Dr R.Buscall Professor R. H. Ottewill Dr T. Cosgrove Professor J. S. Higgins Dr R. W. Richards Dr R. A. L. Jones New experimental methods and new theoretical and computational techniques have recently led to great progress in understanding the difficult but technologically important problems associated with the conformation of polymer molecules at surfaces and interfaces. The purpose of this Discussion is to bring together experimentalists and theoreticians working towards a molecular understanding of polymers at surfaces and interactions to survey the progress in the area to date and to indicate future directions of research.The meeting will attempt to bring a unified approach to the problem, encompassing problems of the structure of surfaces and interfaces in polymer melts, the conformation of polymers at solidniquid and liquidniquid interfaces, and extensions towards more complicated biological systems. The preliminary programme may be obtained from Mrs Angela Fish, The Royal Society of Chemistry, Burlington House, Piccadilly , London W1V OBN. THE ROYAL SOCIETY OF CHEMISTRY, FARADAY DIVISION, GENERAL DISCUSSION 99 Vibrational Optical Activity: from Fundamentals to Biological Applications University of Glasgow, 19-21 December 1994 Organising Committee Professor L.D. Barron (Chairman) Dr A. F. Drake Dr D. L. Andrews Professor R. E. Hester Professor A. D. Buckingham Traditional optical activity measurements such as CD are confined to the visible and near-ultraviolet spectral regions where they provide stereochemical information on chiral molecules via polarized electronic transitions. Thanks to prompting from theory and new developments in instrumentation, optical measurements are now being made in the vibrational spectrum using both infrared and Raman methods. Studies over the past decade on a large range of chiral molecules, from small organics to biological macromolecules, have demonstrated that vibrational optical activity opens up a whole new world of fundamental studies and practical applications undreamt of in the realm of conventional electronic optical activity.The meeting seeks to bring together experimentalists and theoreticians to discuss the current and future experimental possibilities and the development of theories, including ab initio computational methods, which can relate the observations to stereochemical details. The increasing importance now being attached to molecular chirality and solution conformation in the life sciences should also encourage the partipation of biomolecular scientists. The preliminary programme may be obtained from Mrs Angela Fish, The Royal Society of Chemistry, Burlington House, London W1V OBH.xi THE ROYAL SOCIETYOF CHEMISTRY, FARADAY DIVISION, GENERAL DISCUSSION 100 Atmospheric Chemistry: Measurements, Mechanisms and Models University of East Anglia, Norwich, 19-21 April 1995 Organising committee: Professor I. W. M. Smith and Dr J. R. Sodeau (Co-chairmen) Dr R. A. Cox Dr J. C. Plane Dr J. Pyle Professor F. Taylor The priority now given by national governments to the study of atmospheric science confums that our understanding of global climate and compositional changes depends upon measurements in both the laboratory and the field. The data obtained by the experimentalists are then applied by modellers who provide the most significant input into legislative controls on pollution matters. However there have been few opportunities for laboratory and field workers along with the modelling community to attend an "interdisciplinary" discussion in which overall progress in our understanding of specific atmospheric problems is assessed.The object of this discussion is to bring together the researchers in the diverse disciplines that make up atmospheric chemistry so that their individual results and conclusions can be communicated to each other. Some of the key issues to be discussed will include: ozone balances in the atmosphere; heterogeneous processes; the interaction of chemistry and dynamics in determining atmospheric composition and change. Particular reference will be made to the input of data to global models from the use of satellite, airborne and ground-based instrumentation.Contributions are invited for consideration by the Organising Committee covering topics within the area of chemistry, dynamics and modelling in the lower and upper atmosphere. Abstracts of about 300 words should be submitted by 31 May 1994 to: Professor I. W. M.Smith OR Dr R. J. Sodeau School of Chemistry School of Chemical Sciences University of Birmingham University of East Anglia Edgbaston, Birmingham Nonvich B15 2iT, UK NR4 7TJ, UK Full papers for publication in the Discussion volume will be required by December 1994. THE ROYAL SOCIETY OF CHEMISTRY, FARADAY DIVISION, GENERAL DISCUSSION 101 Gels Paris, France, 6-8 September 1995 Organising Committee: Dr J. W. Goodwin (Chairman) Dr R. Audebert Dr R.Buscall Professor M. Djabourov Dr A. M. Howe Professor J. Livage Professor J. Lyklema Professor S. B. Ross-Murphy During the last few years there has been an increase in both theoretical and experimental work on gels as new techniques have been applied to a wide range of gelling systems. Typical of these are gels formed from polymers by both physical and chemical interactions as well as gels formed by inorganic and surfactant systems. The meeting will deal with the structure and dynamics of gels with the latter heading covering both swelling and rheological behaviour. Mixed systems such as polymer/surfactant and polymer/particle gels will also be discussed. The Discussion will bring together experimentalists and theoreticians interested in different types of gelling systems and encourage them to interact and assess the current scene and provide a benchmark for future developments.Contributions are invited for consideration by the Organising Committee. Titles and abstracts of about 300 words should be submitted by 30September 1994 to: Dr J. W. Goodwin, School of Chemistry, University of Bristol, Cantock's Close, Bristol, BS8 1 TS, UK Full papers for publication in the Faraday General Discussion 101 volume will be required by May 1995. xii A European Workshop on the Determination of Surface Area and Porosity of Porous Materials will be held on October 4-5, 1994, in the Congress Centre of Antwerp University (UIA). The Workshop is organized by the Laboratory of Inorganic Chemistry and will cover the characterization of micro-, meso- and macro- porous materials, determination of their specific surface area and pore volume, description of the pore types and pore sizes, etc. The Workshop will give an overview of the recent developments in this research area, especially about new methods to analyse the porosity.These characterizations become very important for the optimization and quality control of porous substrates which are used in many technological areas: adsorption, gas separation, catalysis, quality control of porous materials (zeolites, clays, silica, carbon, ...). Topics that will be discussed are: * Determination of the pore size * Gravimetrical adsorption techniques * Modelling of adsorption and desorption phenomena * Mercury porosimetry * New models for pore size distributions * Characterization of the pore types and pore volume The programme of the Workshop includes oral lectures (and invited speakers), poster sessions, open forum and topical discussions and an extended exhibition by several companies.For further information contact: Mrs M Stalmans Department of Chemistry, Universiteitsplein 1, B-26 10 Wilrijk, Belgium Tel: 32-3-820.23.75 Fax: 32-3-820.23.74 e-mail: evansant@schs.uia.ac.be xiii Russian Chemical Reviews is an authoritative, Russian Chemical Reviews gives you a simple and specialist publication, providing easy access to reviews straightforward route to the achievements of Russian of important new work from Russia and the other chemistry and offers: countries of the former USSR.It is the English edition of the monthly review journal Uspekhi Khimii, 0 High-quality translation of the Russian published by the Russian Academy of Sciences. originals Each issue is approximately 100 pages in length and usually contains five or six specially commissioned 0 Much increased speed of publication review articles. These reviews cover most aspects of modern chemistry, particularly: @ Authoritative editorial control in Moscow and the United Kingdom under the supervision of the Russian Academy of 0 Structure of Molecules and Quantum Sciences and the Royal Society of Chemistry Chemistry 0 Coordination Chemistry 0 Analytical Chemistry 0 Chemical Physics 0 Physical Chemistry including Catalysis 0 Organic and Organometallic Chemistry 0 Chemistry of Macromolecules 0 Biochemistry and Bioorganic Chemistry 0 Materials Chemistry Written by authorities, the reviews are speciallytranslated for Russian Chemical Reviews, edited to the highest possible standard, and published as soon as possible after the Russian-language original.In this way English-speaking scientists from around the world have the rapid access they need to valuable new work originally published in Russian. Russian Chemical Reviews is essential reading for all who value high-quality reviews of current chemical research. Make sure you order your subscription now! To order please contact: ROYAL SOCIETY OF Turpin Distribution Services Ltd, Blackhorse Road, Letchworth, Herts SG6 lHN, UK CHEMI STRY Tel: +44 (0) 462 672555.Fax: +44 (0) 462 480947. Telex: 825372 TURPIN G For further information and a sample issue please contact the: z&f Sales and Promotion Department, Royal Society of ChemistryThomas Graham House, Science Park, Milton Road, Cambridge CB4 4WF, UK Information Tel: 44 (0) 223 420066. Fax: +44 (0) 223 423623. Services CHEMICAL SOCIETY REVIEWS Chemical Society Reviews, recognising the importance of inter-disciplinary dialogue in scientific research, contains reviews which cover a diversity of chemistry topics. 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ISSN:0956-5000    

DOI:10.1039/FT99490BP117

出版商:RSC    

年代:1994

数据来源: RSC

摘要:

J. CHEM. SOC. FARADAY TRANS., 1994, 90(12), 1559-1567 INTRODUCTORY LECTURE Electrostatic Acceleration of the 1,s-H Shifts in Cyclopentadiene and in Penta-I ,3=diene by Li Complexation:Aromaticity of the + Transition Structures Haijun Jiao and Paul von Rague Schleyer" Computer-Chemie Centrum, lnstitut fur Organische Chemie der Universitat Erlangen-Nurnberg , Henkestrasse 42,91054 Erlangen, Germany High-level ab initio molecular orbital calculations reproduce the experimental activation parameters for the 13-H shifts in cyclopentadiene and in penta-I ,3-diene excellently and predict a remarkable electrostatic acceler- ation of both 1,5-H shifts by Li+ complexation. These catalytic effects (8.0 and 5.2 kcal mol-', respectively) are electrostatic in origin: the transition states are more stabilized by Li+ than the ground states. Replacement of Li+ by a positive charge gives similar results.The aromaticity of the transition states was evidenced by various criteria: by the large energies of concert, by C-C bond-length equalization and by the ringcurrent effects: upfield 6Li+ shifts, the deshielding of 6H as well as the exalted magnetic susceptibilities and magnetic aniso- tropies computed using the IGLO method. Among the sigmatropic rearrangement prototypes considered ascribed to Lewis-acid complexation of Li to heteroatoms + by Woodward and Hoffmann,' the thermal 1,5-H shifts in or functional groups present in the dienophile or in the diene. cyclopentadiene and penta-1,3-diene have been well studied Our goal here was different, to investigate theoretically the experiment all^^-^ and the ore tic all^.^-^ The 1,5-H shift tran- acceleration of the 1,5-H shifts in cyclopentadiene and penta- sition structures, Huckel (4n + 2) n-electron arrays, have 1,3-diene by Li+, i.e.in hydrocarbon systems without func- suprafacial topologies. Roth reported the kinetics of the 1,5- tional groups or heteroatoms. We have shown recently that H shift for conversion of [1,2,3,4,5,-2H,]cyclopentadiene to the barrier to the degenerate Cope rearrangement in semi- [2,3,4,5,5-2H,]cyclopentadiene in 1964. For the temperature bullvalene can be eliminated by Li+ complexation due to the range 45-65"C, the Arrhenius equation for this 1,5-H shift greater electrostatic stabilization of the transition over the was K = 1.3 x 10l2exp[-(24.3 & 0.5) k~al/RT].~ Also by gound-state structure.' ' using 'H NMR, Roth and Konig measured the 1,5-H shift in [1,1-2H2]penta-1,3-diene at 185-205 "C; the Arrhenius Computational Details parameters were K = 2.8 x 10°C-(36.3 & 0.5) k~al/RT].~ Calculations were carried out using the GAUSSIAN 92 These 1,5-H shifts are first-order reactions whose rates are Program package.I2 Geometries of all stationary points were not influenced by polar fully optimized at RMP2(fu)/6-3 1G* and characterized as Early ab initio calculations on the 1,5-H shift in cyclo- minima or saddle points by analytic second-derivative com- pentadiene (CPD)7 overestimated the activation energy, but putation of harmonic vibrational frequencies.These provided indicated the reaction to be concerted and the transition the zero-point vibrational energies (ZPE), entropies and ther- structure to have the C, symmetry predicted by Woodward mochemical data. The computed ZPEs were scaled by an and Hoffmann.' The 1,5-H shift in penta-1,3-diene has been empirical factor of 0.93.' Single-point energies were com- studied at much more sophisticated levels (up to puted at the RMP4SDTQ and RQCISD(T) levels using the RMP4SDTQ using larger basis sets) than the 1,5-H shift in 6-31 1G** basis set and the RMP2(fu)/6-31G* ge~metries.'~ CPD. At higher correlated levels, Houk et al. found the The activation enthalpies (AH*) are corrected for ZPE and former 1,5-H shift to be concerted and the calculated activa- thermal energies (vibrational, rotational and transitional tion parameters to be in quite good agreement with the energies) at finite temperatures.' The activation energy (E,) observed value^.^.'^^ is equal to AH* + RT.Natural charges and Wiberg bond Recently, many observations have shown that Diels-Alder indices (Tables 1 and 2) calculated using the natural popu- reactions are accelerated dramatically by e.g. LiC104/diethyl lation analysis (NPA) method of Reed and Weinhold et al., ether lo and similar media. Such accelerations have been helped to characterize the transition structure^.'^ Chemical Table 1 Wiberg bond indices [RHF/6-31G*//RMP2(fu)/6-31G*] for species involved in the 1,5-H shifts in CPD and the CPD-Li' complex and the NPAI4 charges for H(m) point group C(1)-C(2) C(2)- C(3) C( 1)-CC(5) C(5)-H C(5)--H(m) NPA 1.855 1.102 1.032 0.897 -0.2491 c2V 2 C5V 1.320 1.320 1.320 0.912 0.125 0.608 3 1.369 1.459 1.044 0.909 0.410 0.359CS 6 cs 1.821 1.117 1.042 0.892" 0.833b 0.266," 0.332b 7 C," 1.328 1.328 1.328 0.888 0.116 0.645 8 CS 1.352 1.452 1.059 0.880 0.432 0.286 9 c, 1.366 1.453 1.016 0.883 0.3 79 0.493 " cis with regard to Li'.trans with regard to Li+. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 2 Wiberg bond indices [RHF/6-31G*//RMP2(fu)/6-31G*] for the species involved in the 1,5-H shifts in penta-1,3-diene and in its Li’ complex and the NPA14 charge of H(m) point group C(l)-C(2) C(2)-C(3) C(3)-C(4) C(4)-C(5) C(l)-C(5) C(5)-H(m) NPA 4 CS 1.920 1.087 1.039 5 CS 1.384 1.462 1.462 10 Cl 1.912 1.078 1.843 11 c, 1.387 1.448 1.448 12 cs 1.388 1.457 1.457 shifts (SLi’ and SH) and magnetic susceptibilities (x) were computed using the IGLO method” with the BII basis set’6 [constructed from Huzinaga 9s5p set for carbon 51 11 1/21 11, a d-set, q = l.O), 5s set for hydrogen (311, a p-set, q = 0.65) and 9s3p for Li (51111/111, a p-set, q = 0.19, 0.75, 3.0)] and the correlated geometries.Results and Discussion 1,5-H Shift in Cyclopentadiene (CPD) The RMP2(fu)/6-31G* geometries (bond lengths in A and bond angles in degrees) for CPD, 1, and two possible tran- sition structures, 2, in C,, and 3 in C,symmetry, are shown in Fig. 1. According to the RMP2(fu)/6-3 lG* frequency calculations, 1 is the ground state but the highly symmetrical 2 is not a true transition structure since it has two degenerate imagin- ary frequencies (-1822 cm- ’).On the other hand, the C, 3 is the authentic transition structure with only one imaginary frequency (-1192 cm-’) for the Hs migrating from C(5) to C(1). As shown in Fig. 1, the C-C bonds in 1 have the typical alternating lengths of 1.499, 1.353 and 1.463 A for single and double bonds along a conjugated chain; the dis- tances are in excellent agreement with the experimental values (given in par en these^).^^ In the authentic transition structure 3, all C-C bonds [apart from C(l)-C(5), 1.488 A] have nearly the same lengths of 1.400-1.406 A. These are very close to the benzene value, 1.395 8, (computed at the same level).Hence, the transition structure is aromatic according to the geometric criterion of ar~maticity:’~ the C-C bond lengths are equal or nearly equal. The bond to the migrating hydrogen C-H(m) (1.300 A) in 3 has a Wiberg bond index of 0.410, smaller than that (0.897) of the methylene C-H bond (1.099 A) in 1. The natural charge, H(m)-0.359, reveals that the migrating H is only slightly more positive than the methylene H (0.249) in CPD, and it is not ‘protonic’. Hence, the underlying five-carbon skeleton does not resemble an ‘aromatic’ cyclopentadienyl anion in character.’* The other Hs in 3 have natural charges of 0.229-0.259, i.e. nearly the same as in CPD. On the other hand, the C-C bond lengths in 2 are 1.425 A.The charge on the H over the ring is 0.608; hence the C,H, moiety does have considerable cyclo-pentadienyl anion character in this hypothetical form. The C-H distance of this centrally bridging hydrogen is long (1.538 A) and the Wiberg bond index in 2 is only 0.125. The latter is much smaller than that of C-H(m) in the authentic transition structure 3 (Table 1). 1,SH Shift in Penta-1,Miene The RMP2(fu)/6-3 lG* geometries for cis-penta- 1,3-diene7 4 (Cdand the transition structure (TS), 5 (CS) are shown in Fig. 2. At this correlated level, 5 is the authentic transition state (only one imaginary frequency, -1522 cm-’) for the H migration from C(5) to C(1). The geometry of the starting diene, C, 4, has the normal alternating single and double bond lengths (1.498, 1.348, 1.455 and 1.344 A).The configu- 0.o00 0.926 0.2 18-0.229 1.384 0.018 0.448 0.244 1.047 0.o00 0.906 0.243-0.271 1.387 0.032 0.444 0.253 1.388 0.018 0.463 0.142 ration chosen leads directly to the transition structure after cisoid deformation. The situation for the 1,7-H shift in (2,Z)-hepta-1,3,5-triene is ~imilar.’~” The partial C(1)-C(m) bond length of 1.409 8, is longer in 5 than that (1.300 8,)in the 1,5- H shift TS 3 in CPD and in the TS for the 1,7-H shift in hepta-1,3,5-triene (1.352 4.’”The C-C bond lengths in 5 (1.396-1.418 8,) are in the range of the typical C-C separa-tions in the transition structures of many pericyclic reactions, e.g.1.40 8, for the 1,7-H shift TS” and are very similar to the C-C bond length in benzene.”” The C(l)-C(5) distance (2.581 A) in the TS 5 is too long for any significant inter- 0 (106.3’) 1.463A XgA 69.8‘\f3 108.3O 3,Cs Fig. 1 RMP2(fu)/6-31G* optimized geometries for cyclopentadiene (l),the C,, form (2) and the authentic C, transition structure of the 1,5-H shift in CPD (3) J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 b d 5, CS Fig. 2 RMP2(fu)/6-31G* optimized geometries for penta-1,3-diene (4) and authentic transition structure of 1,5-H shift in penta-1,3-diene (5) action between C(l) and C(5), and the C(l)-C(5) Wiberg bond index of 0.018 is very small. The C(l)H(m)C(S) bond angle in 5 is 132.6" and the other CCC bond angles are 119.8" and 122.5", i.e.larger than those in the TS 3 in CPD. The natural charge for the migrating H in 5 (0.244) is less positive than that (0.359) in the 1,5-H shift TS 3 (0.359) in CPD, but is the same as in the 1,7-H shift TS (0.244).'9a The charge on the other Hs (0.228-0.238) in 5 are like those in the ground state (0.204-0.228) (Table 2). Both 1,5-H shift transition states in cyclopentadiene and in penta-1,3-diene fulfil the geometric criterion of aromaticity.' Activation Parameters of 1,5-H Shifts As indicated in Table 4, the computed activation energies for the 1,5-H shift in CPD at RMP4SDTQ and at RQCISD(T) with the 6-311G** basis set and corrected for ZPE and thermal energies at 400 K, are 27.0 and 27.5 kcal mol-' (Tables 3 and 4).Roth's measured value is 24.3 +_ 0.5 kcal mol-'.2 The calculated activation entropy for the 1,5-H shift in CPD is -0.1 cal mol-I K-';whereas the measured value is -3.3 cal mol-' K-' for [*H,]~yclopentadiene.~ The cal- culated frequency factor of 7.9 x 10l2 also agrees reasonably well with the experimental 1.3 x loi2. The calculated relative energy, 65.9 kcal mol-', for the C,, 2 alternative is much too high for 2 to compete as an alternative transition state. The 1,5-H shift activation barriers in penta-1,3-diene are 36.9 and 34.9 kcal mol-' at RQCISD(T)/ and RMP4SDTQ/ 6-311G** corrected to 500 K (Table 4). These values are in excellent agreement with Roth and Konig's experimental value,3 36.3 f0.5 kcal mol- '.The calculated activation entropy, -8.8 cal mol-' K-I, also agrees well with the mea- sured -7.1 cal mol-' K-', as does the computed frequency factor, A = 1.2 x lo", us. the experimental A = 2.8 x 10". These higher-level ab initio calculations reproduce the mea- sured kinetics of the 1,5-H shifts in CPD and in penta-1,3- diene accurately. (Note, however, that tunnelling has not been taken into account). The low activation energies of the 1,5-H shifts contrast with the bond dissociation energy of cu. 75-78 kcal mol- for the C(5)-H bonds both in penta-1,3-diene and in CPD.20 The stepwise reactions, involving the rupture of a C-H bond and the migration of an H radical to the other terminus, are much less favourable. The energy of c~ncert'~ is ca.50 kcal mol-' for the 1,5-H shift in CPD and 40 kcal mol-' in penta-1,3-diene. Hence, the energetic criterion of aromaticity' is fulfilled for the transition structures in both 1,5-H shift processes. Note that the 1,7-H shift has an even lower activation energy Jca. 20 kcal mol-') and a higher energy of concert (ca. 60 kcal mol-')'9a than these two 1,5-H Table 3 Calculated total energies (Eh),LI ZPE (kcal mol- ') and number of imaginary frequencies (NIMAG, given in parentheses) for 1-5 RMP2(fu)/631G*/FOPT ZPEb (NIMAG) RMP2(fu)/6-311G** RQCISD(T)/6-311G** RMP4SDTQ/6-311G** 1 -193.499 67 53.6 (0) -193.536 15 -193.609 36 -193.608 97 2 -193.329 38 49.0 (2) -193.432 19 --193.496 22 3 -193.404 07 51.7(1) -193.495 19 -193.56040 -193.562 42 4 -194.615 30 66.1 (0) -194.72005 -194.805 69 -194.803 74 5 -194.555 27 64.3 (1) -194.665 7 1 -194.741 91 -194.743 14 Single-point energies calculated using RMP2(fu)/6-3 1G* geometries. RMP2(fu)/6-31G* values scaled by 0.93.13 Table 4 Calculated entropies (9,activation entropies (AS*/cal mol- K-'),"relative electronic energies (E) and activation energies (Ehcal mol-given in parenthesis as well as frequency factor (A) compared with the measured values RMP2(fu)/631G*S (AS) RMP2(fu)/6-31G* E (E,) 1 7 1.4 (0.0) 0.0 (0.0) 3 2 71.3 (-0.1) 62.8 ( -3.1) 28.6 (26.4) 75.5 (70.6) 4 exp.82.2 (0.0) (-3.0) 0.0 (0.0) 5 exp. 94.6 ( -8.9) (-7.1) 37.7 (34.6) RMP2(fc)/6-311G** E (E,) 0.0 (0.0) 65.2 (60.3)25.7 (23.5) 0.0 (0.0) 34.1 (31.0) Ref.2. Ref. 3. RQCISD(T)/6-311G** E (E3 0.0(0.0) -29.7 (27.5) 0.0(0.0) 40.0 (36.9) RMP4SDTQ/6-311G** E (E3 A 0.0 (0.0) 70.8 (65.9)29.2 (27.0) 7.9 x 10l2 24.3 f 0.5' 1.3 x 10l2 38.0 (34.9) 1.2 x 10" 36.3 f OSd 2.8 x 10" a At 400 K for 1-3; at 500 K for 4,s. E, = AH* + RT. ' 1562 Table 5 Calculated magnetic susceptibility exaltation [AX(tot)/ppm cgs], activation energies Ecalc(Eexp) and energy of concert (E,,,/kcal mol-') for the 1,5-H shifts compared with the 1,7-H shift, the conro- tatory cyclization of octa-l,3,5,7-tetraene and Diels-Alder reactions reactions AX,W Ecalc(Eexp) Em 1,5-H shift in CPD" -8.9 27.5 (24.3 0.5) 50 1,5-H shift in penta-1,3-diene0 -9.9 36.9 (36.3 & 0.5) 40 1,7-H shift in hepta-1,3,5-trieneb -23.1 19.7 (20.8 & 0.7) 60 buta-1,3-diene + ethenec -19.3 22.4 (23.6) 5.7 cyclopentadiene + ethenec -17.7 17.5 (17.5) 13.7 octa-l,3,5,7-tetraene cyclizationd -12.6 15.0 (17.0) 20 This work.* Ref. 19(a) and references therein. 'Ref. 19(b). * Ref. 26. shift processes (Table 5). The greater flexibility of the hep- tatriene system enables the transition structure to have better orbital overlap and to be reached with less deformation. However, the activation entropy is negative for the 1,7-H shift,"" but is near zero for the 1,5-H shift in CPD. We have found that the transition structures for 1,7-H shift,"" for the conrotatory cyclization of octa- 1,3,5,7-tetraene,* ' and for Diels-Alder reactionslgb to be aromatic (Mobius or Huckel) based on the geometric, energetic and magnetic criteria.The magnetic susceptibility exaltation AX(tot), the activation ener- gies ECale(Eexp)and the energies of concert for the 1,5-H shifts, the 1,7-H shift, the conrotatory cyclization of octa- 1,3,5,7- tetraene and the Diels-Alder reactions are given in Table 5. 1,5-H Shift Acceleration by Li' Complexation In the most stable Li+-CPD complex, 6, Li+ coordinates with the two C=C double bonds [the RMP2(fu)/6-31G* geometry is shown in Fig. 3, along with those for 7-91.The complexation energy in 4 is -24.6 kcal mol-l. The two methylene hydrogens, equivalent in CPD, are designated Heis and H,,,,, with regard to Li+ in 6. The natural charge of Hlrnns (0.332) is more positive than Hcis (0.266), implying greater polarization of the C-HH,,,,, bond.The C-HH,,,,, Wiberg bond index (0.833) is also smaller than that of C-HH,, (0.892) (Table 1). The C-C double bonds (1.366 A) are elongated by 0.013 A related to those in CPD, while the C-C single bond lengths hardly change. The distances from Li' to the double-bonded carbons, 2.326 and 2.333 A, are only slightly longer than Li+-C(l) (2.404 A, Fig. 3). The symmetrical complexation of Li+ with C,, 2 gives C,, 7 which, like 2, has two degenerate imaginary frequencies [-1801 cm-', RMP(fu)/6-31G*] and hence is not a true transition state. The Li+-C distances are all 2.268 A. The critical C-H(m) bond length is 1.539 8, (1.538 A in 2), but H(m) is more positive in 7 (0.645) than in 2 (0.608) (Table 1).Li' can coordinate with transition structure 3 in two ways, to give the cis and trans Li+ complexes, 8 and 9. In the cis-TS 8, Li+ and the migrating H(m) are on the same side of the five-carbon skeleton. In 9, the trans-TS, the migrating H(m) and Li+ are on the opposite sides of the five-carbon ring. According to the RMP2(fu)/6-3 lG* frequency calculations, both cis-TS, 8 (-1102 cm-') and trans-TS, 9 (-957 cm-') are authentic transition states with only one imaginary fre- quency. The C-C bond lengths in 8 and 9 are in the 1.411- 1.417 A range, the benzene-Li' complex C-C distance is 1.410 A at the same level." The C(l)-C(5) separation in 9 (1.505 A) is somewhat longer than corresponding lengths in 3 (1.488 A) and in 8 (1.489 A).The critical C(1)-H(m) distances in 8 (1.3 16 A) are longer, but in 9 (1.290A) are shorter than in 3 (1.300 A) Fig. 3), the Wiberg bond index for C(1)-H(m) is 0.379 in 9, and 0.432 as well as 0.410 in 8 and 3. While shorter bonds normally have a larger bond index and longer J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 7, C5" ti(1) 2.287A 71.4" w 9, cs Fig. 3 RMP2(fu)/6-31G* optimized geometries for the complexes of Li+ with CPD(6), with C,, 2 (7), and with the transition structure for the 1,5-H shift in CPD (8,cis-TS;9, trans-TS) J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 1563 Table 6 Calculated total energies (Eb),Ozero-point vibrational energies (ZPEJccal mol- ') and number of the imaginary frequencies (NIMAG, given in parentheses) for 6-12 ~~ ~~ ~ RMP2(fu)/6- 3 1 G */FOPT ZPEb(NIMAG) RMP2(f~)/6-311G** RMP4SDTQ/6-311G** ~ ~~~ 6 -200.746 69 54.8 (0) -200.826 69 -200.898 70 7 -200.643 87 50.5 (2) -200.740 08 -200.803 73 8 -200.698 15 52.8 (1) -200.781 91 -200.849 69 9 -200.71429 53.1 (1) -200.798 33 -200.865 01 10 -201.905 52 67.4 (0) -202.003 57 -202.086 73 11 -201.846 72 65.2 (1) -201.949 97 -202.026 94 12 -201.852 79 75.5 (1) -201.956 53 -202.034 28 +Li -7.250 49 a Single-point energies calculated using RMP2(fu)/6-3 lG* geometries.RMP2(fu)/6-3 lG* values, scaled by 0.93.' Table 7 Calculated entropies (S), activation entropies (AS*/cal mol-' K-'): activation energies (EJb and the catalytic effects (AEJ com-pared with the calculated values without Li+ complexation at the corresponding levels and complexation energies (kcal mol- ') RMP2(f~)/6-31G* RMP2(f~)/6-31G* RMP2(f~)/6-311G** RMP4SDTG/6-311G** RMP4SDTQ/6311G** S (AS) 'a (''cat) 'a (AEcat) Ea (AEcaJ ECO,.6 80.0 (0.0) 0.0 0.0 0.0 -24.6 7 74.2 (-5.8) 64.5 (59.8) 54.3 (49.6) 59.6 (54.9) -35.8 8 79.0 (-1.0) 28.4 (+2.0) 25.9 (+2.4) 28.6 (+1.6) -23.1 9 77.6 (-2.3) 18.5 (-7.9) 16.0 ( -7.5) 19.0 (-8.0) -32.7 10 98.9 (0.0) 0.0 0.0 0.0 -20.4 11 94.6 ( -4.3) 33.7 (-0.9) 30.4 ( -0.6) 34.3 (-0.6) -20.9 12 89.9 (-8.9) 29.9 (-4.7) 26.1 ( -4.9) 29.7 (-5.2) -25.5 At 400 K for 6-9; at 500 K for 1-12: Single-point calculation using RMP2(fu)/6-31G* geometries. AE,,, = Ea (with Lif) at the correspond- ing level.bonds a smaller bond index, the migrating H(m) in 9 (0.439) with C(l-3) (2.245-2.378 A); the Li-C(4) separation (2.682 is more positive than in 8 (0.286) (Table 1). This implies that 9 A) indicates less effective interaction. Besides C(4)-C(5) (1.497 is a tighter transition state with smaller activation energy that A), the other C-C bond lengths in 10 are longer than those of 3 or 8. in penta-1,3-diene, 4 (Fig. 4). On the other hand, the Li+-C distances in 9 (2.282-2.288 The transition state 5 can form two complexes with Li'. In A) are nearly the same as in 7. In 8, where Li+ coordinates the trans complex, 11, TS-trans, the migrating H(m) and Li+ mainly with C(3) (2.202 A) and with C(2,5) (2.365 A), the are opposite. In the cis complex, 12, TS-cis, Li+ and the Li-H(m) distance is 2.107 A (Fig.3). This suggests that the migrating H(m) are on the same side of the five-carbon plane. complexation in 9 is better than in 8. Li has the same charge In comparison with the transition structure 5, TS-trans 11 (0.967) in all the complexes 6-9. has a shorter C(l)-C(5) separation (2.566 A), but all C-C At RMP4SDTQ(fc)/6-31 l**//RMP2(fu)/6-31G*, the C,, bonds are longer. Li+ coordinates mainly with C(3) (2.170 A) symmetric 7 has the largest complexation energy (E,,, ), and with C(2,4) (2.440 A). The critical C(5)-H(m) bond -35.8 kcal mol-', and five equal Li-C distances (2.268 1). length (1.408 A) and its Wiberg bond index (0.444)are nearly The trans-TS 9, in which the five Li-C distances (2.282- the same in 11 as in the parent transition structure, 5.In 2.288 A) are nearly equal, is computed to have a larger com- contrast, TS-cis 12 has a larger C(l)-C(5) (2.650 A) separa-plexation energy (-32.7 kcal mol-') than that of the tion than complex 11 and transition structure 5. Although Li+-CPD complex, 6 (-24.6 kcal mol-I). Hence, Li+ com- the C(1)-H partial bond of 1.451 A in 12 is longer than that plexation results in a pronounced (8.1 kcal mol-') acceler-in cis complex 11 (1.409 A), C(1)-H(m) in 12 has a larger ation effect in 9. On the other hand, the cis-TS 8, in which Wiberg bond index (0.463) than 11 (0.444).The natural Li+ coordinates mainly with C(2-4), has a smaller Li+ com- charges for the migrating Hs are 0.253 in 11 and 0.142 in 12, plexation energy ( -23.1 kcal mol- I) than 6.Hence, no accel- compared with 0.243-0.271 in 10. The Li charges (0.966- eration can be expected via 8 (Tables 6 and 7). 0.971) are close to unity. The greatest differences between At RMP4SDTQ(fc)/6-31 lG**//RMP2(f~)6-31G* + ZPE TS-cis 12, and TS-trans 11, are the Li+-C separations and (RMP2(fu)/6-31G*) and evaluation to 400 K, trans-TS 9, is the Li+ coordination with the migrating H (1.879 A) in TS-cis computed to have an activation energy of 19.0 kcal mol-'. 12 (Fig. 4). The effect of Li+ coordination, 8.0 kcal mo1-', is nearly the The computed complexation energy for TS-cis 12 (-25.5 same as that at 0 K. The 1,5-H shift in cyclopentadiene is kcal mol-') is larger than that for both TS-trans 11 and 10 strongly accelerated by Li + complexation.At the same level ( -20.9 and -20.4 kcal mol- ',Table 7). The 5.1 kcal mol -the calculated activation energies for the cis-TS 8 is 28.6 kcal difference in the complexation energies between 10 and TS-cis mol-', i.e. 1.6 kcal mol-' higher than without Li+ complex- 12, result in a pronounced acceleration effect. ation. Only trans coordination is effective. According to the RMP2(fu)/6-3 lG* frequency calculations, complex 10 is a minimum, while 11 and 12 are both tran- sition structures for H migration. The calculated activation 1,SH Shift Acceleration in Penta-1,Sdieneby Li+ energy involving 11 is 34.3 kcal mol-l. This is only 0.6 kcal As in the Li+ CPD complex, 6, Li+ coordinates with the two mol-' lower than the reaction without Li+ complexation. C=C double bonds of cis-penta-1,3-diene (4) to give 10 (Fig.Hence, there is no catalytic effect in TS-trans 11. In contrast, 4 shows the RMP2(fu)/6-31G* geometries). Note the s-cis TS-cis 12 is computed to have an activation energy of 29.7 conformation of the diene moiety in 10, and its geometrical kcal mol-', 5.2 kcal mol-' lower than the reaction without relationship to transition structure 11. In 10, Li+ coordinates Li+. Hence, the 1,s-H shift in penta-1,3-diene is accelerated 1564 Li(1) 2.245 A 10, c, nLi(1) Li(1) n 132.0' 12, cs Fig. 4 RMP2(fu)/6-31G* optimized geometries for the complexes of Li+ with penta-ld-diene (10) and with the 1,5-H shift transition structures in penta-l,3diene (TS-trans 11, and TS-cis 12) by Li+ complexation, but only when Li+ and the migrating hydrogen, H(m), are cis to each other.This contrasts with the 1,5-H shift in CPD, where the catalytic effect is found in the trans complex 9 (Table 7). Our calculations indicate that the 1,5-H shifts are acceler- ated by Li+ complexation via the trans transition structure 9 in CPD and via the cis transition structure 12 in penta-1,3- diene. These accelerations reflect the greater electrostatic sta- bilization of the transition states than the ground states by Li'. This was demonstrated by investigating the effect of a J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 positive charge and of the valence orbitals of Li+ both separately and together.The calculated results, for the 13-H shift in CPD at RMP2(fc)/6-3 1 1G**/ /RMP2(fu)/6- 31G* + ZPE [RMP2(fu)/6-31G*, 400 K] and the 1,5-shift in penta- 1,3-diene at RMP4SDTQ/6-3 1 1G**/ /RMP2(fu)/6- 31G* + ZPE [RMP2(fu)/6-31G*, 500 K], are given in Table 8. Since, E, = 23.5 kcal mol-' for the 1,5-H shift in CPD without Li+ (Table 4), and 16.0 kcal mol-' with Li+ com- plexation, the catalytic effect is 7.5 kcal mol- '(Table 7). The calculated E, is 23.1 kcal mol-' after replacement of Li+ by its valence orbitals, i.e. almost the same as the E, without Li+ complexation. When Li' is replaced by a positive charge (+), the calculated E, of 15.1 kcal mol-' is 8.4 kcal mol-' lower than that without Li+ complexation. This lowering is nearly the same as with Li+.Hence, electrostatic interactions are the main contribution to the catalytic effect. After replacement of Li+ by both valence orbitals and a positive charge, the calcu- lated E, of 16.4 kcal mol-' is very close to the value with Li+ itself (16.0 kcal mol-'). In order to check if there are any differential energy effects due to Li' complexation, Li' was left out (replaced by a dummy atom), and the energies of the hydrocarbon residues recomputed at the same geometries. The activation energy, 23.1 kcal mol-l, calculations in this manner, is very close to that (23.5 kcal mol-') for the fully relaxed 1 and 3 (Table 8). Since the Li+ catalysis in 6 and 9 is only electrostatic, we investigated the 1,5-H shift in penta-1,3-diene less extensively, only by replacing Li+ by a positive charge in 10 and 12.The same effects are found as in CPD: the 5.0 kcal mol-' acceler-ation effect due to a positive charge is close to that in the Li+ complex 12 (5.2 kcal mol-'). Hence, the main contributions also come from the electrostatic interactions (Table 8). Magnetic Criteria of Aromaticity of the 1,SH Transition States The 1,5-H transition states are aromatic according to the geometric and energetic criteria of aromaticity:' '*19 they have nearly equal C-C bond lengths and large energies of concert (Table 5). The magnetic properties of these 1,5-H transition states fulfil the magnetic criterion of aromaticity as well. The SHand SLi' chemical shifts as well as the magnetic suscepti- bility exaltation (Ax) were calculated using IGLO15 method and the Huzinaga BII basis set.16 That aromatic compounds exhibit enhanced diamagnetic susceptibility was noted by Pascal in his pioneering investiga- tions." Pauling ascribed these effects to ring currents in 1936.21~22Dauben et aLZ3used the magnetic susceptibility exaltation and Flygare and co-~orkers~~ the magnetic sus- ceptibility anisotropies to characterize the aromatic com-pounds comprehensively.Recently, Cremer et established that homo- and bishomo-cations were aromatic by means of their computed magnetic susceptibilities. In a new development and application, our group is character- izing pericyclic transition states as being Huckel and Mobius aromatics, by computing the exaltation of the magnetic sus- ceptibilities between transition-and ground-state struc-tures.' 8*26 Even though magnetic properties of transition states cannot be measured experimentally, they can be calcu- lated easily.'5*'8,27 We now examine the magnetic criteria here.As summarized in Fig. 5, the S'H [IGLO/BII//RMP2(fu)/ 6-31G*] for the vinyl hydrogens 6.4 and 6.6 in CPD agree well with the measured values (6.4 and 6.5), whereas the methylene hydrogens (2.1) differ by 0.8 ppm from the experi- mental chemical shifts (2.9). In the C,, 2, the chemical shifts for the nearly in-plane hydrogens are 6 = 6.5, where the J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 8 Calculated total energies (EJ, activation energies (EJkcal mol- I) and analyses of Li+ complexation catalytic effects RMP2(f~)/6-3 1 1G** a 6 9 Ea JL.+Li +(valence)b -193.534 82 -193.494 78 23.1 -0.4 Li+ +(+)' -193.596 76 -193.569 53 15.1 -8.4 +Li +(+,valence)d -193.670 08 -193.640 81 16.4 -7.1 Li+ -+ (dummy)' -193.534 82 -193.494 78 23.1 -0.4 RMP4SDTQ/6-311G** 10 12 'a 4.t. Li+ +(+)' -194.857 36 -194.80460 29.9 -5.0 a Single-point calculations using RMP2(fu)/6-31G* geometries of the Li+ complexes. Li' replaced by its valence orbitals (valence). Lif replaced by a positive point charge (+). Li+ replaced by both its valence orbitals and a positive point charge (+, valence). 'Li+ left out (replaced by a dummy atom). capping hydrogen is strongly deshielded (18.8 ppm). This is 'equatorial' H and 0.9 for the 'axial' H which lies in the inner opposite to the upfield shift expected due to the ring-current cone and experiences shielding ring-current effects. The calcu- effects (cf.6Li in CpLi). We attribute this deshielding to the lated magnetic susceptibility exaltation of -9.9, which is exceptionally large charge (0.608) on this hydrogen. In the smaller than that in the 1,7-H shift transition structure authentic transition state 3, 6'H = 1.6 for the migrating (-23.1),"" and the exalted magnetic anisotropy of -31.5, hydrogen is close to the value in CPD, where 6lH = 7.8 indicate that the transition state has aromatic character. C(3)-H is deshielded to a greater extent than the Hs in Hence, the 1,5-H shift transition structures, both in CPD and benzene (6lH = 7.2 at the same level).The C(l)-C(5) Hs in in penta-1,3-diene, are aromatic, not only according to the transition structure 3 are deshielded; their average value, geometric and energetic, but also the magnetic criteria of 6H = 6.3, is larger than those in CPD (5.6 ppm). The cyclic aromatici ty . ' delocalization is larger in the transition structure 3 than in We have employed 6Li+ as another aromaticity probe. CPD. This conclusion is supported by the diamagnetic sus- The Li+ resonance is shifted upfield in many LiT-complexes ceptibility exaltation of -8.9 and the exalted magnetic of aromatic systems due to strong ring-current effects.' 'J* anisotropy (-19.0), both relative to 1. For example, the Li+ upfield shift is computed to be -6.9 in The calculated 6Hs for the 1,5-H shift TS in penta-1,3- cyclopentadienyl lithium (the experimental value is diene are given in Fig.6. The terminal Hs at C(l) [or C(5)l 6Li = -8.6, measured in THF at 25 "C) and -10.8 in the have two very different chemical shifts, 4.1 ppm for sandwiched biscyclopentadienyllithium anion (6Li = -13.1 1.6 x(dia, para. n.1.) (-57.6, +6.2,+0.4) (-66.7, +8.2, +0.8) (-65.0, +6.4, -1.3) x(tot.)/Ax(tot.) -51 .O/O.O -57.7/-6.7 -59.9/-8.9 x(anis.)/Ax(anis.) -31 .O/O.O -53.8/-22.8 -5O.O/-19.0 Fig. 5 IGLO calculated chemical shifts (#H, in ppm; the measured values for CPD are given in parentheses) and magnetic susceptibilities (x) (diamagnetic, paramagnetic and non-local contributions, ppm cgs) and their exaltations [Adtot)] for the 13-H shift in CPD at the IGLO/BII// RMP2(fu)/6-3 lG* level 5.11C(1) (75) 1.1 5.2 6.6 1.7 x(dia.para. n.1.) (-61.2, -61 ., +1.7) (-70.4 + 6.1, +1 .O) x(tot.) /Ax( tot.) -53.4/0.0 -63.31-9.9 X(anis.)/Ax(anis.) -1 6.8/0.0 -48.31-31.5 Fig. 6 IGLO calculated chemical shifts (6' H,in ppm) and magnetic susceptibilities (x) (diamagnetic, paramagnetic and non-local contribu- tions, ppm cgs) and their exaltations [A;c(tot)] for the 1,5-H shift in penta-1,3-diene at the IGLO/BII//RMP2(fu)/6-3lG* level J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 0,96.0 0,101.8 0, 100.1 0, 101.0 -0.6 -6.4 -4.7 -5.6 1.5 7, C5" x(dia. para, n.1.) x(tot.)/Ax(tot.)x( anis)/Ax( an is) -51.5/0.0 (-58.9, +7.1, +0.3 -33.4 (-67.8, +7.9, 0.0) -59.8/-8.3 -51.7/-18.3 (-65.3, +6.7, -0.7) -59.3/ -7.8 -45.8/-12.4 (-65.6, +6.5, -1.4) -60.5/-9.0 -49.9/-16.5 Fig.7 IGLO-calculated absolute Li+ shielding constants (a/ppm), chemical shifts (6'H, SLi+ relative to Li+ = 0.0, ppm) and magnetic suscep tibilities (x) (diamagnetic, paramagnetic and non-local contributions, ppm cgs) and their exaltations [Ax(tot)] for the Li+ acceleration of 1,5-H shift in the CPD-Li+ complex at the IGLO/BII/ /RMP2(fu)/6-3 lG* level 0. 92.8 6,96.6 0. 103.1 +2.6 -1.2 -7.7 7 5.5 X(dia, para, m.1.) (-61,9, +7.3, +3.0) (-72.2, +8.5, +1.3) (-71.7, +6.3, +1.0) x(tot.)/Ax(tot.) -51.2/0.0 -62.3,'-11.1 -64.4/-13.2 x(anis)/Ax(anis) -1 4.5/0.0 -46.5/-32.0 -49.9/- 35.4 Fig. 8 IGLO-calculated absolute Li+ shielding constants (cppm), chemical shifts (dlH, 6Li' relative to Li+ = 0.0, ppm) and magnetic suscep tibilities (x)(diamagnetic, paramagnetic and non-local contributions, ppm cgs) and their exaltations [Ax(tot)] for the Li+ acceleration of the 1,5- H shift in the penta-1,3-diene-Li+ at the complex IGLO/BII//RMP2(fu)/6-3 lG* level ppm, measured in THF at -107 oC).27a In our study of the Note that the transition state with the lower activation degenerate Cope rearrangement in semibullvalene, the upfield energy has larger magnetic susceptibility exaltation and Li+ shift of -10.8 in the lithium cation complex reflects the larger Li+ upfield shift in case of Li+ complex.The more strong ring-current effects in the bishomoaromatic transition favourable transition state is indeed more 'aromatic '! state." Li+ has a normal chemical shift of -0.6 in Li+-CPD 6, but in the C,, structure 7 (with NIMAG = 2), 6Li+ is -6.4.Cyclopentadiene In the cis-TS 8 (-4.7) and the trans-TS 9 (-5.6) 6Li+ shield- The possibility that the pseudo 271. CH, electrons could con- ed values are also found. The calculated magnetic suscepti- tribute hyperconjugatively to give CPD aromatic character bility exaltations, -7.9 for the cis-TS 8 and -9.0 for the has been considered for some time.23a This deserves separate trans-TS 9 relative to the Li+-CPD complex 6, and the comment. Although the heat of formation does not reveal exalted magnetic anisotropies (-12.4 and -16.5, any significant stabilization, Flygare noted that CPD has an respectively), also indicate that the Li+-complexed transition unusually large magnetic susceptibility ani~otropy.~~ Using states are aromatic (Fig.7). their increment system, Dauben et al.23a' found cyclo-Nearly the same situation pertains to the Li+ species pentadiene to have a magnetic susceptibility exaltation of involved in the accelerated 1,5-H shift of penta-1,3-diene (Fig. -6.5 ppm cgs attributable to cyclic delocalization. Recently, 8). For example, the Li+ chemical shift is +2.6 in the Kutzelnigg et supported the aromaticity of CPD based complex of Li' with penta-1,3-diene, 10, but is -1.2 in 11 on the exalted magnetic anisotropy computed by IGLO. and -7.7 in 12 (this upfield shift is even larger than that in However, our estimate of the magnetic susceptibility exalta- the Li+-benzene complex, -6.6 ppm, computed at the same tion of -2.0 is smaller than that of Dauben et and is in level).The aromaticity of the Li+-complexed transition struc- the normal range. Moreover, cyclopentadiene (-51.0) has tures also is indicated by the magnetic susceptibility exalta- nearly the same magnetic susceptibility as (Z)-penta-1,3-diene tions of -11.1 for 11 and -13.2 for 12 as well as by the (-53.4) which has two more Hs. Cyclopentadiene does have exalted magnetic anisotropies of -32.0 and -35.4, respec- a larger magnetic anisotropy (-31.0) than penta-1,3-diene tively. (-16.8), but similar behaviour is found in cyclopropene and J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 1567 Table 9 Calculated magnetic susceptibilities, dtot) and magnetic anisotropies, X(anis) cgs ppm (IGLO/BII//RMP2/6-31G*) G.Evans and M. Polyanyi, Trans. Faraday SOC., 1938, 34, 11; M. G. Evans and E. Warhurst, Trans. Faraday SOC., 1938, 34, compound point group dtot) AX(tot)" X(anis)b 2 614; M. G. Evans, Trans. Faraday SOC., 1939,35,824. W. R. Roth, Tetrahedron Lett., 1964,20, 1009. benzene D6h -68.0 0.0 -52.9 3 W. R. Roth and J. Konig, Justus Liebigs Ann. Chem., 1966, 24, 699 hexa-1,3,5-triene cs -59.1' +8.9 -26.3 cyclopen tadiene c2v -51.0 0.0 -31.1 4 C. W. Spangler, Chem. Rev., 1976, 76, 187, and references therein. penta-1,3-diene cs -53.4' -2.4 -16.8 cyclopropene c2v -31.7 0.0 -18.9 propene cs -35.4' -3.7 -7.3 5 6 K. N. Houk, Y. Li and J.D. Evanseck, Angew. Chem., 1992,104, 711; Angew. Chem., Int. Ed. Engl., 1992,31,682. B. A. Hess, Jr., L. J. Schaad and J. Pancir, J. Am. Chem. SOC., AX(tot) = X(tot, open chain) -X(tot, cyclic compound). X(anis) = ~(33,out of plane) -i[x(11) +~(22),in plane]. Note that the open-chain molecules have two more Hs than the cyclic compounds; each hydrogen contributes ca. -2 ppm cgs to X(tot). 7 1985,107,149. (a) N. G. Rondan and K. N. Houk, Tetrahedron Lett., 1984, 24, 2519; H. Jiao, Diplomarbeit, Erlangen, 1992; S. M. Bachrach, J. Org. Chem., 1993, 58, 5414; (b) D. Damiani, L. Ferretti and E. Gallinella, Chem. Phys. Lett., 1976, 37, 265. 8 F. Jensen and K. N. Houk, J. Am. Chem. SOC., 1987, 109, 3139; propene. Cyclopropene (-31.7) has nearly the same magnetic susceptibility as propene (-35.4, which has two more Hs), but the former (-17.0) has larger magnetic anisotropy than 9 D.D. Kahn, W. J. Hehre, N. G. Rondan and K. N. Houk, J. Am. Chem. SOC., 1985,107,8192. M. J. S. Dewar, E. F. Healy and J. M. Ruiz, J. Am. Chem. SOC., 1988, 110, 2666; M. J. S. Dewar, K. M. Merz Jr. and J. J. P. the latter (-6.3) despite having two fewer hydrogens.28 Stewart, J. Chem. SOC., Chem. Commun., 1985, 166; Y-P. Liu, G. Benzene not only has larger magnetic susceptibility (-68.0), but also larger magnetic anisotropy (-52.9) than hexa-1,3,5- triene [x(tot), -59.1 and X(anis), -26.31 [IGLO/BII/ / RMP2(fu)/6-31G*] (Table 9). Benzene has equal C-C bond lengths and hexa- 1,3,5-triene has alternating single and double bonds.However, as shown in Fig. 1 and 2, the C-C 10 C. Lynch, T. N. Truong, D-H. Lu, D. G. Truhler and B. C. Garrett, J. Am. Chem. SOC., 1993, 115,2408. R. Braun and J. Sauer, Chem. Ber., 1986, 119, 1269; R. Breslow and T. Guo, J. Am. Chem. SOC., 1988, 110, 5613; H. Waldmann, Angew. Chem., 1991, 103, 1335; Angew. Chem., Int. Ed. Engl., 1991, 30, 1991; M. A. Forman and W. P. Dailey, J. Am. Chem. SOC., 1991, 113, 2761; A. Casachi, G. Desimoni, G. Faita, A. G. bond lengths in cyclopentadiene are nearly the same as in (Z)-penta-1,3-diene (1.353 us. 1.348 A, and 1.463 us. 1.455 A as well as 1.499 us. 1.498 A, respectively), despite the differences in substitution and angles. Based on the homodesmotic equa- tions which should correct for strain, the stabilization energy of cyclopentadiene, 2.4 kcal mol- (evaluated with cyclo- Invernizzi, S.Lanati and P. P. Righetti, J. Am. Chem. SOC., 1993, 115, 8002; P. A. Grieco, J. J. Nunes and M. D. Gaul, J. Am. Chem. Soc., 1990, 112, 4595; G. Desimoni, G. Faita, P. P. Righ- etti and G. Tacconi, Tetrahedron, 1991, 47, 8399; P. A. Grieco, Aldrichim. Acta, 1991, 24, 59; R. M. Pagni, C. M. Kabalka, S. Bains, M. Plesco, J. Wilson and J. Bartmess, J. Org. Chem., 1993, 58, 3130, W. Srisiri, A. B. Padias and H. K. Hall Jr., J. Am. pentene and cyclopentane), is less than that of (2)-penta-1,3-diene, 4.0 kcal mol -[evaluated also using experimental data with pentane, pent-l-ene and (Z)-pent-2-ene].28*29 The SLi+ in complex 6 is not shielded hence the energetic, structural, and magnetic criteria are ambiguous with regard to the idea 11 12 Chem.SOC., 1993,58,4185. H. Jiao and P. v. R. Schleyer, Angew. Chem., Int. Ed. Engl., 1993, 32, 1760. GAUSSIAN 92, Revision B, M. J. Frisch, G. W. Trucks, M. Head-Gordon, P. M. W. Gill, M. W. Wong, J. K. Foresman, B. G. Johnson, H. B. Schlegel, M. A. Robb, E. S. Replogle, R. Gom- that cyclopentadiene might be aromatic. perts, J. L. Andres, K. Raghavachari, J. L. Binkley, C. Gonzalez, R. L. Martin, D. J. Fox, D. J. Defrees, J. Baker, J. J. P. Stewart Conclusions 13 and J. A. Pople, Gaussian, Inc., Pittsburgh PA, 1992. W. J. Hehre, L. Radom, P. v. R. Schleyer and J. A. Pople, Ab High-level ab initio computations are able to reproduce the experimental activation energies for the 1,5-H shifts in cyclo- pentadiene and in penta-1,3-diene and to confirm the predic- tions of Woodward and Hoffmann.The aromaticity of the 1,5-H shift transition structures are evidenced by the structur- al, energetic and magnetic criteria. The determination of the 14 15 initio Molecular Orbital Theory, Wiley, New York, 1986. A. E. Reed, L. A. Curtiss and F. Weinhold, Chem. Rev., 1988,88, 899; A. E. Reed and P. v. R. Schleyer, J. Am. Chem. SOC., 1990, 112,1434. W. Kutzelnigg, M. Schindler and U. Fleischer, NMR, Basic Principles and Progress, Springer Verlag, Berlin, 1990, vol. 23, p. 165. magnetic properties of the transition structures is a new application of IGLO computations. Ring-current effects are responsible for deshielded and shielded hydrogen and lithium chemical shifts as well as exalted magnetic susceptibilities.Li+ complexation stabilizes the transition-state structures more strongly than the ground-state structures. The former 16 17 S. Huzinaga, Approximate Atomic Wave Functions, University of Alberta, Edmonton, Alberta, 1971;S. Huzinaga, Gaussian Basis Setsfor Molecular Caclufations, Elsevier, Amsterdam, 1984. P. J. Garratt, Aromaticity, Wiley, New York, 1986, 11, p. 295; W. v. E. Doering and T. Sachdev, J. Am. Chem. SOC., 1975, 113, 4288; W. v. E. Doering, W. R. Roth, R. Breuckmann, L. Figge, H-W. Lennartz, W-D. Fessner and H. Prinzbach, Chem. Ber., are more polarizable.? Hence, remarkable electrostatic accel- erations of 15-H shifts result. 18 1988, 121, 1. S. McLean and P. Haynes, Tetrahedron, 1965, 21, 2329; K. S. This work was supported by the Deutsche Forschungs-gemeinschaft (DFG), by the Fonds der Deutschen Industrie, by the Stiftung Volkswagenwerk and by the Convex Com- puter Corporation. We also thank the Shanxi Normal Uni- 19 Replogle and B. K. Carpenter, J. Am. Chem. SOC., 1984, 106, 5751; E. M. Schulman, A. E. Merbach, M.Turin, R. Wedinger and W. J. Le Noble, J. Am. Chem. SOC., 1983,105,3988. (a) H. Jiao and P. v. R. Schleyer, Angew. Chem., Znt. Ed. Engl., 1993, 32; (b) R. Herges, H. Jiao and P. v. R. Schleyer, Angew. Chem., 1994, in the press. versity (China) for a scholarship (to H. J.). 20 J. J. Gajewski, Hydrocarbon Thermal Isomerizations, Academic Press, New York, 1981, vol. 44. t Polarizability computations at the RMP2(fc)/6-31G*//RMP2(fu)/ 21 Pascal, Ann. Chim. Phys., 1910, 19, 5; L. Pauling, J. Chem. Phys., 1936, 4, 673. 6-31G* level show a significantly greater ayytensor for 3 than for 1. 22 C. K. Ingold, Structures and Mechanisms of Organic Reactions, G. Bell and Sons, London, 1953, pp. 185-196; A. Pacault, Ann. References 23 Chim., 1946, 1, 567. (a)H. J. Dauben Jr., J. D. Wilson and J. L. Laity, J. Am. Chem. 1 B. R. Woodward and R. Hoffmann, Angew. Chem., 1969, 81, 797; Angew. Chem., Int. Ed. Engl., 1969, 8, 781; The Conserva- tion of Orbital Symmetry, Verlag Chemie, Weinheim, 1970; M. SOC., 1968, 91, 811; (b) H. J. Dauben Jr., J. D. Wilson and J. L. Laity, J. Am. Chem. SOC., 1969, 92, 1991, (c) H. J. Dauben Jr., J. D. Wilson and J. L. Laity, in Nonbenzoid Aromatics, ed. J. P.

ISSN:0956-5000    

DOI:10.1039/FT9949001559

出版商:RSC    

年代:1994

数据来源: RSC

摘要:

J. CHEM. SOC. FARADAY TRANS., 1994, 90(12), 1569-1574 Some Thoughts on Reaction-path Following H. Bernhard Schlegel Department of Chemistry, Wayne State University, Detroit, MI 48202, USA Errors in reaction-path following have been examined with the aid of a simple model surface and a local correction scheme has been proposed. Two new fourth-order explicit methods for reaction-path following have been developed, and two potential-energy surfaces with analytical reaction paths have been constructed. Some aspects of reaction-path bifurcation are also discussed. In exploring a potential-energy surface for a reaction, nor- mally the first step is to optimize the geometry of the relevant stationary points, i.e. the reactants, transition structure and products.' To confirm a reaction mechanism, it may be necessary to prove that the particular transition structure found in the optimization connects the desired reactants and products.This can be done by following the path of steepest descent downhill from the transition structure toward the reactants and toward the products. Following the reaction path can also show whether the mechanism involves any intermediates between reactants and products. Although the path of steepest descent depends on the coordinate system, a change in the coordinate system does not change the nature of the stationary points and does not alter the fact that the energy decreases monotonically along the reaction path from the transition structure toward reactants or products. Thus any coordinate system can be used to explore the mechanism of a reaction.One system, mass-weighted Cartesian coordi- nates, has special significance for reaction dynamics, and the path of steepest descent in this coordinate system is called the intrinsic reaction coordinate (IRC).2 The next step in characterizing a reaction in a theoretical study of a potential-energy surface is to calculate the rate of the reaction. At the simplest level, one can use conventional transition-state theory (TST), which depends on the geometry and vibrational modes of the transition str~cture.~If the barrier is low or broad, the dynamic bottleneck may not be at the transition structure, and one needs to use variational transition-state theory (VTST).4 This requires the reaction path or IRC near the transition state and the vibrational fre- quencies perpendicular to the path.Tunnelling corrections may also be important and can be estimated from the IRC and the shape of the potential-energy surface near the tran- sition state. Following reaction paths is, therefore, central to any treat- ment of reactions on potential-energy surfaces that goes beyond locating transition structures. Methods for comput- ing reaction paths have been reviewed recently.'m6 Despite their conceptual simplicity, reaction paths are remarkably dif- ficult to follow efficiently and accurately. Many small steps may be needed to follow the path closely, and this can be quite costly if the potential-energy surface is obtained by high-level ab initio electronic structure calculations.The reason for these difficulties is that the defining equations for reaction paths belong to a class of stiff differential equations. With this short paper we hope to stimulate discussion by offering two new fourth-order path-following methods, some new test surfaces and a few thoughts on bifurcation of reac- tion paths. Definitions A potential-energy surface E(x)can be expanded as a Taylor series about xo E(x)= Eo + &(x -xO) + +(x -xO)'HO(X -~0) * .* (1)+ where E,, go and H, are the energy, gradient and Hessian at x, . The reaction path on this surface can also be expanded as a Taylor series 4s) = 40)+ u0(0)s + +U1(0)S2 + * * * (2) where s is the arc length along the path, no is the tangent vector, and u1 is the curvature.The tangent vector for the path of steepest descent is (3) The curvature can be computed for the Hessian: nl(s) = -[Hao-(oO'HUO)OO]/~~(X) 1; IC = I I' I (4) At the transition structure, the gradient is zero and the tangent is given by the eigenvector of the Hessian corre- sponding to the negative eigenvalue, and the curvature is given by d(s) = -[H -~(u~'H~~)/~-'[F'u~-(o~'F'o~)o~](5) where F:j = ck Fjjk u: and Fijk are the third derivatives. A number of quantities are needed for treatments of reac-tion rates that go beyond conventional transition-state theory. The vibrational frequencies perpendicular to the reac- tion path can be obtained by diagonalking the projected Hessian: =HPloj PHP; P = I -uOUO' (6) The coupling terms between motion along the path and vibrational modes perpendicular to the path are given by: (7) where L are the eigenvectors of the projected Hessian.For- mulae for other terms appearing in the VTST and reaction- path Hamiltonian treatments of reaction rates can be found in the literature.'^^ Bifurcation Bifurcation is a novel aspect of reaction paths and has been discussed extensively by Ruedenberg9 and others. A potential-energy surface in which one valley divides into two has a valley-ridge inflection point (VRI). On one side of the VRI, all second derivatives perpendicular to the reaction path are positive, indicating a valley; on the other side, one per- pendicular mode has a negative eigenvalue, indicating a ridge.Thus, the VRI is characterized by a zero eigenvalue for the second derivatives perpendicular to the path. Baker and Gill" have published an algorithm for locating VRIs on 1.0 0 Fig. 1 Model potential-energy surface showing a bifurcating valley and a VRI. Two paths of steepest descent, displaced a small distance either side of the VRI follow the ridge for a considerable distance beyond the VRI before diverging. potential-energy surfaces calculated by electronic structure methods. Although Ruedenberg has clearly stated that the valley, not the reaction path, divides at the VRI, there may still be a general misconception that the reaction path also splits in two at the VRI.Ruedenberg has pointed out that the path does not bifurcate at a VRI unless it is a stationary point, and that for a non-stationary point, the path of steepest descent follows the ridge. Even when they are displaced a small amount to either side of the ridge, paths of steepest descent follow the ridge for a considerable distance before diverging (see Fig. 1). By way of comparison, note that paths infinitesimally displaced either side of the valley converge. The dilemma is then to develop a concept of a bifurcating reaction path that follows the valleys and not the ridge. For a normal path of steepest descent, one can think of a marble rolling down the potential-energy surface very slowly (e.g. in molasses). We suggest for a bifurcating path, one 1.0 -0 Fig.2 A family of paths descending on a model potential-energy surface with a bifurcating valley and a VRI. A hard-sphere potential prevents the paths from coming closer than a preset minimum dis-tance. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 should consider a pair of marbles, side by side, rolling slowly down the surface. The hard-sphere repulsion keeps them separated by a fixed distance and the paths are parallel to the path of steepest descent until the VRI is reached. After the VRI, the paths diverge, as shown in Fig. 2. The rate of diver-gence depends on the distance from the ridge, the slope along the path and the vibrational modes perpendicular to path. This concept can be generalized to many hard-sphere test particles descending on a surface.The resulting paths are similar to streamlines in incompressible fluid flow. For a wavepacket following the path, it is perhaps better considered as compressible fluid and to replace the hard-sphere potential with a softer repulsive potential [e.g. l/r, l/r2, exp(-ar2)]. One could even speculate that it may be possible to choose a form of this repulsion so that the streamlines correspond to lines of equal probability along a wavepacket trajectory. Relation between Errors in the Reaction Path, Tangent, Curvature and Projected Frequencies A little work with a model potential can reveal some inter-esting connections between various errors encountered in reaction-path following. Consider a simple two-dimensional linear trough : 0 E(x, y) = --ax + 4by2; 47 = (-4by); ”=[b0 “1 Let the previous, current and next points on the reaction path be x-= (-c, 0),xo = (-0, 0) and x1 = (c, 0);for each point the tangent and curvature are vo = (1, 0) and v1 = (0, 0), respectively.Consider an error in the lateral position of the current point, xb = (0, Ay). The tangent and curvature at this point can be found by substituting into eqn. (3) and (4): (a, -b AY)0’0 = J(u2 + b2 Ay2) = (COS8, -sin 8); tan 8 = b Ay/u (9) v’l = -(0,-b sin e) -b sin2 e(C0s 8, -sin 8) J(u2 + b2 Ay2) b cos 8 sin 8 --J(u2 + b2 Ay2) (sin 8, cos 8) = rc(sin 8, cos 6) (10) For small displacements such that u2 9 b2 Ay2, the tangent and the magnitude of the curvature are approximately v” = (1, -b Aylu); K = b2 Ay/u2 (11) Thus the error in the tangent is a factor of b/u times the error in the coordinate of the reaction path.This factor can be sig-nificantly larger than 1 if u, the gradient along the path, is small (e.g. near the transition state) and/or if b, the second derivative perpendicular to the path, is large (e.g. a narrow valley). The amplification factor for the error in the curvature is the square of the factor for the tangent, indicating that it is even more difficult to compute accurate values for the curva-ture, and quantities that depend on it, such as the coupling coefficients in eqn. (7). The relative error in the projected fre-quency mo -0 ~(b)~(b-cos2 e) b2 Ay2-J(b) = 1 -cos 0 = -2u2 (12)00 is smaller than the error in the tangent, since b Ay/u < 1.The errors in the normal modes are similar to the error in the tangent vector. This analysis suggests that the coordinates of the reaction path need to be determined quite accurately near the tran-sition state where the gradients are small, and for those in J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 perpendicular mode with large force constants. This also sug- gests some strategies for improving the calculations. For first-order methods, one can obtain a suitable estimate of the tangent from the displacement tan 8 = -Ay/c (13) This will lead to an improvement in the curvature and pro- jected frequencies if l/c < b/a.Note that the errors in doand (xb -x-')/I xb -x-I are opposite in sign; if the two factors are comparable in magnitude, an improved estimate of the tangent is If subsequent points along the path have already been calcu- lated, a better estimate can be obtained by central difference: For higher-order explicit methods for reaction-path follow- ing, such as LQA and CLQA," the estimated tangent analo- gous to eqn.(13) can be obtained by integrating the path and averaging the tangent of the integrated path and the calcu- lated tangent, e.g., $?st = (0" + t&A)/I 0'' + I (17) An improved estimate in the spirit of eqn. (15) can be obtained by matching the path integrated forward from the previous point and backward from the next point, and averaging the two tangents.This approach can be taken one step further to calculate a local correction to the coordinates of the reaction path, based on the gradient and Hessian, and the estimated tangent from above. This can be done by minimizing in the space perpen- dicular to the estimated tangent : AxO = -Hi 'Cgo -(&o,",Ju,",J (18) go = -@o + Ho &o)/lgo + Ho Ax0 I (19) The new tangent and the current Hessian can then be used to calculate improved estimates of the curvature and projected frequencies. It should be emphasized that the effect of this correction is to clean up small errors in the path coordinates, and not to increase the order of the reaction-path following method. If eqn. (14), or its higher-order analogues such as eqn. (16), are used to estimate the tangent, this approach can be viewed as a generalization of the stabilization method used to improve the behaviour of the Euler method for reaction-path following." New Fourth-order Methods for Reaction-path Following Numerical methods for integrating differential equations can be divided into two categories. For implicit methods, the step taken depends on the gradient at the end of the step, whereas for explicit methods it does not.Following reaction paths by the latter technique is computationally simpler and algo- rithms that have been used include Euler's method, the Ishida-Morokuma-Komornicki or stabilized Euler method 1571 (IMK or ES),', Runge-Kutta and predictor-corrector methods,' the local quadratic approximation (LQA),' ' LQA with cubic correction (CLQA),' ' and the Sun-Ruedenberg modification of LQA.14 These methods employ a fixed number of calculations per step; some require only gradients and must take relatively small steps; others use second deriv- atives and have somewhat greater stability.Implicit methods are more difficult to implement, since the end-point of a step must be found by an optimizati~n.'~?'~In return, these methods are more stable than explicit methods and can perform well with larger step sizes. Implicit methods for reac- tion path following include the Muller-Brown method (implicit Euler),' the second-order method of Gonzalez and Schlegel' (implicit trapezoid) and higher-order implicit methods by Gonzalez and Schlegel.16 For use with variational transition-state theory and reaction-path Hamiltonian calculations, it is highly desirable to combine the stability of implicit methods yet avoid the constrained optimization used to determine the end-point of a step.The method should also be higher than second order (so that larger steps can be taken) and use the gradient and Hessian at each point on the path (since the rate calculations need the Hessian at each point). We have combined ideas from the local corrections discussed above and from various implicit and explicit methods to devised two new fourth- order reaction-path following algorithms. Method 1 combines an LQA predictor step" with a cor- rector step based on the fourth-order method F of Gonzalez and Schlegel.I6 The LQA step is obtained by integrating a local quadratic approximation for the gradient from xl, the current point on the path to xi: dr(s) -g; + H;(x -xi) where g; and H; are the gradient and Hessian calculated at xi, a point near xl.The gradient and Hessian, g; and HI2,are then calculated at x;. Eqn. (3) and (4) are used to calculate ~'(0)and v'(0) from g, z g; + H;(x, -xi) and H, x H;; likewise n0(s) and ul(s) are calculated from g, x g; + H',(x2 -xi) and H, x H;. Then x2 is adjusted iteratively until eqn. (21) (the defining equation for method F16)is satisfied, x, = XI + 3[O0(O) + U0(S)]S + +[Ul(O) -u'(s)Js2 (21) where s is chosen to minimize I x2 -xi I. Because method F is correct to fourth order, the resulting step from x1 to x2 is also fourth order, provided that Ixl -x; I and Ix, -xi I are sufficiently small so that local quadratic approximations around x; and xi are valid.Method 2 combines an LQA step with an integration on a quartic surface. The LQA step from x1 to x; and the calcu- lation of g; and H, are the same as in method 1. A quartic energy surface (cubic surface for the gradient) is constructed by fitting to the gradients g;, g; and the Hessians H; and H; . dx) = (g; + H;C(x -4)-t(xi -x;)I}fl(t) + N;K -X;)f,(t) + (8; + &[(x -x;) -(1 -txx; -xi)]} x f'(1 -t) + H'gx; -x'z)f,(l -t) (22) t = (X -x;)(x; -xi)/]X; -X; l2 fl(t) = 1-3t2 + 2t3; f2(t)= t -2t2 + t3 This approximation for the gradient is used in eqn. (3) and the reaction path between x1 and x2 is obtained by inte- grating the differential equation using an accurate numerical method such as the Bulirsch-Stoer method." Both methods outlined above are fourth order, but they have different contributions from higher-order terms.Since they use the same information g1,g;, H;, H2),one can readily compute the step along the path by both methods. The difference between the two paths gives an estimate of the error in the reaction-path following. If this error estimate is outside the acceptable range, the size of the next step can be adjusted accordingly. If the corrections to the LQA step become sizeable, it may be better to calculate x; by the CLQA method,’ or by integrating the quartic approx-imation from the previous step.Test Surfaces for Reaction-path Following Four surfaces are considered in this section: the quadratic and helical valleys are special because they are treated exactly by the LQA and second-order Gonzalez-Schlegel methods, respectively; the Fresnel and logarithmic spirals are impor- tant because they have a very simple dependence on the cur- vature on the reaction path. A quadratic surface for testing reaction-path following is almost trivial, but is of some interest because the path can be obtained analytically, and because the LQA algorithm (and any method derived from it) is exact for this class of surfaces. For simplicity, consider a two-dimensional surface where the eigenvectors of the Hessian aligned with the axes and the minimum is at the origin; the surface, path of steepest descent, tangent and curvature are: E = +ax2 + +by2; g = (ax, by) (23) x(s) = [x, exp(-ut), yo exp(-bt)]; ds -= J[a2xi exp(-2at) + b2yi exp(-2bt)]dt [-ax, exp(-at), -by, exp(-bt)]no = J[a2xi exp(---ut) + b2yi exp(-2bt)] = (COS 8, sin 8) by, b-utan 8 = -exp[-(b -a)t]; -d8 = --sin 28ax0 dt 2 dvovl=-=----duo d8 dt -@in 8, -COS 8)ds d8 dt ds Fig. 3 shows a typical path.For equal displacements along both axes, the descent is first along the mode with the largest eigenvalue until the gradient for this mode becomes compa- rable to the gradient along the other modes. Thus, many of the regions of high curvature seen in reaction paths arise when the descent along one mode is nearly complete and the path turns to descend along another mode.The magnitude of the curvature, K, reaches a maximum near 8 = n/4, and the value at the maximum depends primarily on the difference in the eigenvalues. A series of incrementally more challenging test functions can be constructed to have analytical reaction paths with the following properties: (a) zero curvature [K = 0, a linear trough, eqn. (S)], (b) constant curvature (K = constant, circu- lar helix), (c) curvature linearly dependent on the arc length (ic = as, a Fresnel spiral) and (d)curvature inversely depen- dent on the arc length (ic = a/s, a logarithmic spiral). J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 4’ 3. 2. -1 0 1 2 3 4 Fig.3 A simple quadratic surface showing a path of steepestdescent. The maximum curvature depends on the difference in the eigenvalues. A circular helix, shown in Fig. 4, is a three-dimensional curve with constant curvature, IC, and torsion, z. We have devised a simple potential whose reaction path is a circular helix : -2absin 8, = --(1 + a2)d X(S) = (ro cos 8, ro sin 8, ae); s = eJ(r; + a2) (28) v0(s) = (-r, sin 8, r, cos 8, a)/,,/@; + a2) (29) d(s) = (-r, cos 8, -ro sin 8, O)/(ri+ a2); K = r,/(ri + u2) (30) The second-order and fourth-order method F of Gonzalez and Schlegel are exact for this class of surfaces if they are started on the path, but methods such as LQA, CLQA and 0 Fig. 4 Three-dimensional contour for the helical valley, eqn. (27)with a = l/n, b = 0 and c = 4d J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 traditional numerical methods for integrating differential equations are not. Integration of the appropriate equations for K = .ns leads to the Fresnel integralslg x(s) = [C(s), S(s)]; C(s) = [cos nx2/2 dx; S(s) = [sin nx2/2 dx (31) tt0(s) = (COS 8, sin 8); 8 = ns2/2 (32) d(s) = K( -sin 8, cos 8); K = 71s (33) The reaction path, a Fresnel spiral, is shown in Fig. 5 and for large s has the limiting behaviour of r28 = const. Despite the simple functional form of K, none of the reaction-path algo- rithms devised so far (including method F) is exact for the Fresnel spiral. A logarithmic spiral is obtained if one integrates the equa- tions of K = a/s, where s is the distance from the centre of the spiral.We have constructed a simple energy surface with a logarithmic spiral as a reaction path. -r cos(Y 8, )]+ c In r-+ (34) sin 8, = -2ac/(1 + a2)b x(s) = exp(aO)(cos 8, sin 8); s = ,/(l + a2)exp(a8)/a (35) oo(s) = (a cos 8 -sin 8, a sin 6 + cos 8)/,/(1 + a2) (36) --a sin 8 -cos 8, a cos 8 -sin 0d(s) = C(1 + a2)exPwl ; K = a/s (37) The surface is shown in Fig. 6. Like the Fresnel spiral, none of the reaction-path methods developed to date are exact for the logarithmic spiral. Fig. 6 shows a contour plot of the surface and compares reaction-path following methods 1 and 2 of the present work 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.2 0.4 0.6 Fig. 5 A Fresnel spiral, x = [C(s),S(s)] [see eqn.(31)-(33)] 40 \ -10 0--10 --20 { 1 J -1 0 0 10 20 30 40 Fig. 6 Contour plot of a logarithmic spiral valley [eqn. (34), a = 4,b = 1, c = i]and a comparison of reaction-path following methods 1 (0)and 2 (0)with LQA (+), second-order GS ( x) and the exact path (---) with the LQA method of Page and McIver, the second-order methods Gonzalez-Schlegel and the exact path. When the valley is broad and the curvature small compared to the step size, then all methods behave quite well. As the valley becomes narrower and more curved, methods 1 and 2 perform better than LQA. All of the methods eventually fail when the valley becomes too high and curved for a given step size. Summary A number of thoughts on reaction-path following have been collected together in this paper.To address the dilemma of bifurcation, we offer the concept of a set of hard-sphere test particles descending the surface, tracing out paths akin to streamlines, that follow the bifurcating valleys. We have used a simple model to analyse errors in reaction-path following and have proposed a local correction method that is a gener- alization of the Euler stabilization approach. We have devel- oped two new fourth-order reaction-path following methods that make maximal use of the gradient and Hessian at each step. Lastly, we have examined a number of test surfaces and devised two new potentals with analytical reaction paths. References 1 J. B. Foreman and A. Frisch, Exploring Chemistry with Eiec- tronic Structure Methods, Gaussian Inc., 1993.2 K. Fukui, Acc. Chem. Res., 1981, 14,363. 3 J. I. Steinfeld, J. S. Francisco and W. L. Hase, Chemical Kinetics and Dynamics, Prentice-Hall, New Jersey, 1989. 4 D. G. Truhlar and M. S. Gordon, Science, 1990,249,491. 5 M. L. McKee and M. Page, Rev. Cornput. Chem., 1993,4,35. 6 H. B. Schlegel, in Modern Electronic Structure Theory, ed. D. R. Yarkony, World Scientific Publishing, Singapore, in the press. 7 D. G. Truhlar and B. C. Garrett, Acc. Chem. Res., 1980,13,440. 8 W. H. Miller, N. C. Handy and J. E. Adams, J. Chem. Phys., 1980,72,!39. 9 P. Valtazanos and K. Ruedenberg, Theor. Chim. Acta, 1986,69, 281. 10 J. Baker and P. M. W. Gill, J. Cornput. Chem., 1988,9,465.1574 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 11 M. Page and J. M. McIver, J. Chem. Phys., 1988, 88, 922; M. Page, C. Doubleday and J. W. McIver, J. Chem. Phys., 1990,93, 5634. 16 17 18 C. Gonzalez and H. B. Schlegel,J. Chem. Phys., 1991,95,5853. K. Muller and L. D. Brown, Theor. Chim. Acta, 1979,53,75. W. H. Press, B. P. Flannery, S. A. Teukolsky and W. T. Vetter- 12 13 K. Ishida, K. Morokuma and A. Komornicki, J. Chem. Phys., 1977, 66, 2153; M. W. Schmidt, M. S. Gordon and M. Dupuis, J. Am. Chem. SOC., 1985,107,2585. B. C. Garrett, M. J. Redmon, R. Steckler, D. G. Truhlar, K. K. 19 ling, Numerical Recipes, Cambridge University Press, Cam- bridge, 1989. M. Abramowitz and I. A. Stegan, Handbook of Mathematical Functions, Dover Press, New York, 1965. 14 Baldridge, D. Bartol, M. W. Schmidt and M. S. Gordon, J. Phys. Chem., 1988,92, 1476; K. K. Baldridge, M. S. Gordon, R. Steck- ler and D. G. Truhlar, J. Phys. Chem., 1989,93,5107. J. Q. Sun and K.Ruedenberg, J. Chem. Phys., 1993,99,5257. 20 S. Wolfram, Mathematica, Addison Wesley, London, 1988, and associated computer programs were used to carry out the calcu- lations and prepare the plots in this paper. 15 C. Gonzalez and H. B. Schlegel, J. Chem. Phys., 1989, 90, 2154; C. Gonzalez and H. B. Schlegel,J. Phys. Chem., 1990,94,5523. Paper 3/05186B; Received 27th August, 1993

ISSN:0956-5000    

DOI:10.1039/FT9949001569

出版商:RSC    

年代:1994

数据来源: RSC

摘要:

J. CHEM. SOC. FARADAY TRANS., 1994, 90(12), 1575-1579 Prediction of Whole Reaction Paths for Large Molecular Systems Shirley S-L. Chiu, Joseph J. W. McDouall* and Ian H. Hillier Department of Chemistry, University of Manchester, Manchester, UK M 13 9PL Reaction pathways for large systems such as proteins or other macromolecules are difficult to model using standard methods owing to the many degrees of freedom in such systems. Standard Euler-type methods which require knowledge of a transition structure, from which the path to two energy minima may be obtained are very inefficient when a whole reaction path is required since only small steps may be used with such methods. Furthermore, the location of a transition may itself be very difficult for large systems. Given these problems, an alternative approach (as suggested by Elber and Karplus, Chem.Phys. Left., 1987, 139, 375), based on mini- mizing a functional of the entire path appears very attractive. This approach has not, previously, been evaluated for quantum-mechanical reaction surfaces, only for molecular mechanical surfaces. The assessment of a scheme, based on the Elber-Karplus approach, within both an ab inifio and semi-empirical molecular orbital framework is presented. The method is evaluated by comparing the predicted paths with those obtained by the much used Gonzalez-Schlegel method for three model systems (isomerization of HCN, SN-2reaction of F-and CH,F and the addition of HF to ethene). The method is also tested on reactions without a transition state (hydride attack on an ester and a thioester).In the latter case, the conventional methods are more difficult to apply. The extension of the method to describe reactions in solution is discussed. In discussions of the process of chemical change in polyato- In following the change in molecular properties across a mic systems, the reaction path concept holds a central place. surface, it is not essential to obtain an exceptionally accurate Fukui put forward a general definition of the reaction path as representation of the path since most properties will not be the path of steepest descent, in mass-weighted Cartesian coor- significantly affected by small changes in geometry. Hence, we dinates, that connects the transition state with the reactant have investigated the use of an alternative strategy based on valley in one direction and the product valley in the opposite the method of Elber and Karplus6 (EK) in which the reaction direction.' This is usually termed the intrinsic reaction coor- path is obtained by minimizing a functional of the whole dinate.The significance of the Fukui definition is that this is path. The theory of the approach is outlined in the following the path that a reactive system would follow classically if the section and then tested by comparison with the widely used rcaction were to take place infinitely slowly. Miller and co- Gonzalez-Schlegel method.' Finally, two examples of reac-workers have developed models of dynamics in polyatomic tions which proceed without a barrier, in the gas phase, are molecular systems based on the intrinsic reaction coordinate2 presented.The simulation of reactions in solution is also These models give an interesting explored by using various continuum models to solvateand modifications there~f.~ representation of the dynamics as motion along the reaction points along the gas-phase reaction path. coordinate coupled to harmonic vibrations orthogonal to the path. The Fukui definition can be extended to any coordinate Theory system by simply defining the reaction path as the minimum- We begin by briefly reviewing the EK method.6 Consider the energy path connecting reactants and products via the tran- line integral sition state. Recently we have been interested in obtaining reaction lr[~(~)paths for a diverse range of systems, not with a view to pur- S(Ri 3 Rf)L = .~~(R)IL (1) suing dynamical studies but rather to enable us to map out the evolution of certain molecular properties (e.g.vibrational where E(R) is the total energy of the system in the Born- frequencies, charges, multipole moments) during the course of Oppenheimer approximation, dependent on R,the nuclear a reaction. Traditional methods for obtaining a reaction position vector. dl(R) is a line element on the path L of length path4 begin by finding the transition state and walking L between the initial and final configurations, Ri and R,, downhill towards reactants and products. Since the gradient respectively. The purpose is then to find the path Lthat mini- is zero at the transition state the initial descent direction is mizes S(Ri, Rf)L.Introducing M intermediate grid points, taken to be the transition vector, which necessitates the eqn. (1) can be written in discretized form as evaluation of the second-derivative matrix. To map the whole lM reaction path requires many energy and gradient evaluations s(R, 9 R, + 1)L = -C E<Rj>* Alj (2) since small steps must be used to avoid straying from the L j=1 minimum-energy path. For some methods5 second-derivative In eqn. (2), the constant contribution from the initial and information is also required at several points along the path. final points (R, = Ri, RM+l= Rf) is omitted and Rj is the These matters serve to make reaction path following a difi- value of R at the endpoint of the interval Afj,where cult undertaking for large molecular systems since a tran- Uj,j-= Alj*Uj,j-(3)sition state may not be easily located and it may be Alj = J(Rj -Rj-1)2 impractical to obtain second derivatives of the potential- and Uj,j-l is a unit vector in the direction Rj -Rj-The energy surface to define the initial descent direction.The situ- total path length is given by ation is further complicated in the case of reactions with no Mf1transition state (e.g. hydride attack on the carbonyl group of L = 1Alj (4)an ester in the gas phase). j= 1 EK recognized that a straightforward minimization of eqn. (2) would lead to two problems. The first arises from the fact that the lowest value of S(R,, RM+l)Lwilt be obtained if all of the grid points moved to the initial or ha1 configurations.This would be possible if there was no constraint put on the values of Afj and would lead to a nonsensical representation of eqn. (1). Secondly, for large molecular systems it is very much easier to work in Cartesian coordinates. However, if Cartesian coordinates are used in an optimization procedure, then global translation and rotation of the system will be coupled with the internal displacements. EK overcame these difficulties by introducing two penalty functions to eliminate uneven path segments and rigid-body motions. In our pre-liminary work with this method we used the original EK for-mulation but found that it led to difficulties in convergence.The minimization of the original EK functional was found to be extremely sensitive to the choice of penalty multipliers. In addition it was found that a suitable value of a penalty multi- plier for a molecular mechanical potential was quite unsuit- able for a semiempirical potential which in turn was unsuitable for an ab initio potential. For bimolecular prob- lems the scheme was found to be essentially unworkable, since the main part of the optimization effort went into mini- mizing the penalty functions rather than the potential energy. To overcome these problems we chose to eliminate the uneven path segments and the rigid-body motion explicitly at each point in the optimization. This was achieved by redistributing the grid points along the path such that they were evenly distributed (see Fig.1). To obtain an even redis- tribution of the grid points it was assumed that the position vector Rj transformed linearly into Rj+1. Rigid-body motion was eliminated by taking the first atom of the system as being located at the origin, allowing the second atom of the system to move only in the z-axis and the third atom to move only in the zx-plane. These constraints were applied to all points along the path, hence eliminating global rotation and trans- lation. Once these conditions had been applied, eqn. (5) (which represents the mean energy of the reaction path) was minimized using a conjugate gradient algorithm.8 This minimization method was chosen since it does not require the generation, storage or updating of second-derivative informa- tion.The procedure is usually started by assuming that the reactant and product configurations are connected by a linear synchronous transit (LST) path. If the true reaction path deviates substantially from the LST path, as will usually be the case, the centre point of the reaction path will be much further away from the LST path than those points close to the two minima (see Fig. 2). If all the points on the path are allowed to have the same step size, the optimization becomes insensitive to displacements near the end points and these can then oscillate around the path causing instability in the method (particularly if the potential is very flat in this region).This can be avoided by damping the displacements. However, applying uniform damping to all points leads to slower con- vergence since the points farthest from the path are damped by the same amount as those close to the path. A better strat- egy is to use a differential damping in which the points near the end configurations are more heavily damped than those far away. The procedure outlined above performs quite reliably as will be shown in the next section. However, note that in reac- tions for which multiple transition states exist and hence multiple reaction paths exist, the current procedure will con- J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 h !5Lu Ro R, R2 __. ._. .__ ___ '.' RM RM+l Fig. 1 Reaction profile showing evenly distributed grid points n 'minim urn-energy path Fig.2 Contour surface showing the deviation of the linear synchro- nous transit path from the true reaction path on a curved surface -8ol ,#---"*> 1I I I I i ll I I 0 2 4 6 a 10 reaction coordinate lm4 i * 0 0.8 Q)4-0.6E 0 0.4 4 0.21 ; o k I I 1 -A -1 .o 0 1.o 2.0 z-coordinate of H atom/8c Fig. 3 (a) Energy profile for HCN isomerization. (b) Path of the H atom in HCN isomerization. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 verge to the path nearest to the initial guess. To find alterna- tive reaction paths it is necessary to alter the initial guess so as to sample different regions of the potential-energy surface.Note that there is no guarantee that the current method will yield a path that passes exactly through the transition-state geometry because the transition-state geometry is obtained from the maximum in the energy profile which will typically be an interpolated value. To ensure that the path does pass through the transition state exactly, the transition state (when known) can be used as the configuration R, and the reactants/products as R,, 1. This algorithm has been pro- grammed and interfaced with the GAUSSIAN 92' and MOPAC 6.0" suites of programs. Test Cases In this section we illustrate our method and compare it with the Gonzalez-Schlegel (GS) appr~ach.~ The GS method is now widely used and provides a good measure of the per- formance of our method.HCN Isomerization This reaction has been studied extensively and used to test transition-state optimization methods and reaction-path algorithms. At the HF/STO-3G level the optimized geometry of the reactant (HCN) is R, = 1.153 A, R, = 1.070 A. The product (HNC) geometry is R,, = 1.170 A, R, = 1.010 A. Nine intermediate points were used and eqn. (5) was opti- mized after six iterations. The energy profile is plotted in Fig. 3(a). The maximum point was determined by a spline fit of reaction coordinate the energy profile and the transition state was estimated to have the following geometry RCN= 1.221 (1.221) A, R, = 1.190 (1.202) A and 8HCN = 72.74 (72.77)'. The numbers in parentheses refer to the geometry obtained from the fully optimized transition structure.The difference in energy between the exact transition structure and that found by our method is 0.05 kcal mol- Fig. 3(b) shows the path of the hydrogen atom during the isomerization. The dashed line represents the path obtained by the GS method and the circles represent the optimized grid points obtained by our method. The agreement for this simple reaction is very good. S,2 Reaction: F-+ CH,F + FCH, + F-This identity reaction provides a good test of our method and we studied this at the ab initio HF/3-21G and semiempirical AM1 levels of theory. At the HF/3-21G level, the reaction path was calculated between the two ion-dipole complexes where RCF(l)= 1.448 A, = 2.308 A, R,, = 1.068 A and OHCF(1) = 109.5'.Again, nine intermediate points were used and damping was introduced to improve convergence. The reaction profile obtained is shown in Fig. qa). Fig. 4(b) com-pares the change in the two C-F distances during the course of the reaction as predicted by our method and the GS method. The transition structure was obtained from the maximum point of the energy profile and found to have the following geometry = 1.781 (1.775) A, R~~(~)= 1.781 (1.775) A, R, = 1.062 (1.062) 8, and eHCF(1) = 90.0 (90.0)O. The exact geometry of the transition state is given in parenth- 35 30 -I 25-m9 20 r P 15 -.-a E lo al c a5 0 reaction coordinate Fig. 4 (a) Energy profile for F-+ CH,F +FCH, + F-reaction at the HF/3-21G level.(b) Variation of C-F distances for F-+ CH,F + FCH, + F-reaction at the HF/3-21G level. (c) Energy profile for F-+ CH,F + FCH, + F-reaction at the AM1 level. (d) Variation of C-F distances for F-+ CH,F + FCH, + F-reaction at the AM1 level. 1578 eses and the energy difference between the two structures is 0.02 kcal mol -Fig. 4(c) shows the corresponding energy profile obtained at the AM1 level and the C-F variation is shown in Fig. qd).The estimated geometry of the transition state at the AM1 level is &(I) = 1.624 (1.602) A, RCF(,)= 1.624 (1.602) A, Rc, = 1.124 (1.131) A and &CF(1) = 90.0 (90.0)o. The difference in energy between the approximate and exact transition structures is 0.22 kcal mol- '. The discrep- ancy between our method and the GS method is greater in the case of semiempirical wavefunctions.To obtain these results it was necessary to specify the ANALYTIC option for the gradients in the AM1 method, otherwise a quite erratic energy profile is obtained. Addition to Alkene: HF + C,H, +CH,CH,F This reaction is an example of a four-centre addition reaction and is complicated by the fact that the HF moiety approaches the alkene double bond in an eclipsed orientation but the product geometry corresponds to the staggered con- figuration of ethylfluoride. Hence the path is highly curved once the transition state has been crossed. The reaction path was obtained at the HF/STO-3G level. The reactant configu- ration corresponded to the optimized structures of ethene and hydrogen fluoride separated by 3.3 A.Nine intermediate points were used and damping was again applied. The results are given in Fig. 5. The transition structure estimated from the energy profile has geometry R,, = 1.060 (1.026) A, RcF = 1.715 (1.671) A, 140 120 r I-;100 -m 80 > F 60 a 0 2 4 6 8 10 reaction coordinate 3.0 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 R, = 1.418 (1.404) A and 8ccF = 91.4 (93.2)'. The maximum difference in bond length is 0.045 A and 1.8' in bond angles between the exact transition state and the estimated struc- ture. The corresponding energy difference is 2.83 kcal mol- '. This larger discrepancy can be remedied by employing more intermediate points to obtain a sharper representation of the path, Alternatively, the path can be broken into two separate calculations going from reactants to the exact transition state first and then from the exact transition state to the product.Application to Reactions without a Transition State The reaction studied here is the attack of hydride ion on the carbonyl group of a thioester, specifically CH,COSCH, + H-+CH,CHO + CH,S-This reaction was studied at the HF/3-21G* and AM1 levels of theory. The reactant configuration was taken to have the hydride 3.8 A away from the carbonyl carbon and in the product the sulfur atom was placed 5.4 A from the carbonyl carbon. Seventeen intermediate points were used. These reac- tions are generally thought to proceed through a tetrahedral intermediate.In this instance no tetrahedral intermediate exists at the ab initio level, although a long-range ion-dipole complex does exist [see Fig. qa)]. At the semiempirical level a tetrahedral intermediate does exist [see Fig. qb)]. Similar results were obtained by Howard and Kollmanll (at the ab initio level), who studied gas-phase nucleophilic attack of hydroxide ion and hydrosulfide ion on formaldehyde. They 100 I I 40 4 *a.0-....*-*-*-*-*-*-*-* 0-I 11111111~11111111 I I I 1 1 .o 1.5 2.0 2.5 3.0 0 2 4 6 8 10 12 14 16 18 reaction coordinate RH-FIA Fig. 6 (a) Energy profile for CH,COSCH, + H-+CH,CHO Fig. 5 (a) Energy profile for HF + C,H, --* CH,CH,F reaction. (b) + CH,S-reaction at the HF/3-21G* level.(b) Energy profile for Variation of H-F and C-F distances for HF + C,H, -+ CH,CH,F CH,COSCH, + H-+CH,CHO + CH,S-reaction at the AM1 reaction. level. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 401 .$ -20 c. -40 found no stationary point corresponding to a tetrahedral intermediate in the hydrosulfide + formaldehyde reaction, but did find a stable intermediate in the analogous hydroxide + formaldehyde reaction. The configuration of the ion-dipole complex was estimated from the energy profile, Fig. 6(a).The distance between the sulfur atom of the leaving group and the carbonyl carbon was estimated to be 3.47 A. The ion-dipole complex was then fully optimized and this distance increased to 3.74 A with a corresponding energy lowering of 5.06 kcal mol-'.Thus the product configuration chosen by us was not well suited to reproduce the geometry of the complex; however, the exis- tence of the complex was clearly shown in the energy profile and the optimized geometry easily obtained subsequently. Clearly a more accurate reaction path would result by split- ting the calculation between reactants and the complex and then between the complex and the products. Application to Reactions in the Condensed Phase There is increasing interest in the use of molecular orbital methods to study chemical reactions in the condensed phase. Here the quantum-mechanical part of the system is 'embedded' in an environment which may be modelled explicitly using empirical force fields, or implicitly using con- tinuum models.The former treatment has led to various implementations of hybrid quantum-mechanical, molecular mechanical methods,' whilst continuum methods, particu- larly directed towards modelling solvation, have been imple- mented within both semi-empiri~al'~ and ab initid4 molecular orbital schemes. The strategy of obtaining the reaction path, described in this paper, is of particular value in the context of these condensed phase models, where second derivatives of the energy may be dificult to evaluate. To illustrate the change in reaction path induced by solva- tion we have studied the simple reaction CO, + OH-HCO;4 Previous theoretical studies of this reaction in the gas phase showed no activation barrier.15 However, solvation of struc- tures along the path, using explicit water molecules modelled via molecular dynamics Gibbs energy perturbation simula- tions predicted a solvent induced barrier of 17 & 2 kcal mol-',16 to be compared to an experimental value of 13.5 & 0.2 kcal mol-'.16 We have generated the gas-phase path for this reaction at the ab initio 6-311 + +G** level using the method described herein and solvated structures along the path using the self-consistent reaction field (SCRF) method including a multipole expansion for the solute charge distribution up to the dipole level (I = 1) and a spherical solvent cavity, using GAUSSIAN 92.' An extension of this model up to 1 = 7 for the solute charge distribution and the use of an ellipsoidal cavity has been developed by Rivail and co-workers' ' and implemented with GAUSSIAN 92.The resultant reaction profiles using these two variants of the SCRF method are shown in Fig. 7. In both cases a barrier to reaction is predicted, the barrier heights being 22.0 f 1.1 and 23.7 & 1.1 kcal mol-I for the 1 = 1 and 1= 7 calculations, respectively. These are in satisfactory agreement with the molecular dynamics results, considering that the latter were carried out using a gas-phase reaction path calculated with a correlated (MP4) wavefunction. l6 We thank the Computational Science Initiative of SERC for the provision of workstations on which the present work was carried out, and Shell Research Ltd., for the award of a stu-dentship to S.S.L.C.References 1 K. Fukui, Ace. Chem. Res., 1981,14, 363. 2 W. H. Miller, N. C. Handy and J. E. Adams, J. Chem. Phys., 1980,72,99. 3 B. A. Ruf and W. H. Miller, J. Chem. Soc., Faraday Trans. 2, 1988,84,1523. 4 H. B. Schlegel, Adu. Chem. Phys., 1987,67,249. 5 M. Page and J. W. Mclver Jr., J. Chem. Phys., 1988,88,922. 6 R. Elber and M. Karplus, Chem. Phys. Lett., 1987,139,375. 7 C. Gonzalez and H. B. Schlegel, J. Chem. Phys., 1989,90,2154. 8 W. H. Press, B. P. Flannery, S. A. Teukolsky and W. T. Vetter- ling, in Numerical Recipes, Cambridge University Press, New York, 1986. 9 GAUSSIAN 92, M. J. Frisch, G. W. Trucks, M. Head-Gordon, P. M. W. Gill, M. W. Wong, J. B. Foresman, B.G. Johnson, H. B. Schlegel, M.A. Robb, E. S. Replogle, R. Gomperts, J. L. Andres, K. Raghavachari, J. S. Binkley, C. Gonzalez, R. L. Martin, D. J. Fox, D. J. DeFrees, J. Baker, J. J. P. Stewart and J. A. Pople, Gaussian Inc., Pittsburgh PA, 1992. 10 J. J. P. Stewart, MOPAC, QCPE, 1983, program no. 455. 11 A. E. Howard and P. A. Kollman, J. Am. Chem. SOC., 1988, 110, 7195. 12 A. Warshel and M. Levitt, J. Mol. Biol., 1976, 103, 227; M. J. Field, P. A. Bash and M. Karplus, J. Comput. Chem., 1990, 11, 700; U. C. Singh and P. A. Kollman, J. Comput. Chem., 1986, 7, 718; B. Waszkowycz, I. H. Hillier, N. Gensmantel and D. W. Payling, J. Chem. Soc., Perkin Trans. 2, 1991,225. 13 M. Karelson, T. Tamm, A. R. Katritzky, S. J. Cat0 and M. C. Zerner, Tetrahedron Comput. Methodol., 1989,2,295. 14 0. Tapia and 0. Goscinski, Mol. Phys., 1975, 29, 1653; S. Miertus, E. Scrocco and J. Tomasi, Chem. Phys., 1981, 55, 117; M. W. Wong, M. J. Frisch and K. B. Wiberg, J. Am. Chem. SOC., 1991,113,4776. 15 B. Jonsson, G. Karlstrom and H. Wennerstrom, J. Am. Chem. SOC., 1978, 100, 1658; J-Y. Liang and W. N. Lipscomb, J. Am. Chem. SOC., 1988,108,5051. 16 2.Peng and K. M. Merz Jr., J. Am. Chem. SOC., 1992,114,2733. 17 J. L. Rivail and B. Terryn, J. Chim. Phys., Phys.-Chem. Biof., 1982,79, 2; D. Rinaldi, Comput. Chem., 1982,6, 155; D. Rinaldi, J. L. Rivail and N. Rguini, J. Comput. Chem., 1992, 13,675. Paper 3/04730J; Received 4th August, 1993

ISSN:0956-5000    

DOI:10.1039/FT9949001575

出版商:RSC    

年代:1994

数据来源: RSC

摘要:

J. CHEM. SOC. FARADAY TRANS., 1994, 90(12), 1581-1598 What Woodward and Hoffmann Didn't Tell Us: The Failure of the Born-Oppenheimer Approximation in Competing Reaction Pathways Gabriela C. G. Waschewsky, Phillip W. Kash, Tanya L. Myers, David C. Kitchen and Laurie J. Butler The James Franck Institute and Department of Chemistry, The University of Chicago, Chicago, lL 60637, USA The experiments presented here identify a class of organic reactions, allowed by overall electronic symmetry but WoodwardHoffmann forbidden, in which the failure of the Born-Oppenheimer approximation results in a marked change in the expected branching between energetically allowed chemical bond fission channels. We first review crossed laser-molecular beam experiments on the competition between photodissociation pathways in bromoacetyl and bromopropionyl chloride at 248 nm and bromoacetone at 308 nm.In the com-petition between C-CI and C-Br fission in Br(CH,),COCI, the barrier to C-Br fission on the lowest 'A" potential-energy surface is formed from a weakly avoided electronic configuration crossing, so that non-adiabatic recrossing of the barrier dramatically reduces the branching to C- Br fission. The experimental results and supporting ab initio calculations investigate the strong intramolecular distance dependence of the electronic configuration interaction matrix elements which split the adiabats at the barrier to C-Br fission. The second set of experiments reviewed investigates the competition between C-C and C-Br bond fission in bromoacetone excited in the '[n(O), .n*(C=O)] absorption, elucidating the role of molecular conformation in influencing the probability of adiabatically traversing the conical intersection along the C-C fission reaction coordinate.The paper finishes by presenting new experiments on the photodissociation of chloroacetone at 308 nm which test the conclusions of the earlier work. Photofragment velocity and angular distribution measurements show that C-C fission competes with C-CI fission in this molecule, while only C-CI fission occurs in acetyl chloride upon '[n(O), n*(C=O)] excitation. We investigate two contributing factors to understand the difference in branching. Ab initio calculations show that the splitting at the avoided crossing between the no.nE=o and the npc, a%=, configurations which forms the barrier to C-CI fission is smaller, on average, in trans-chloroacetone than in acetyl chloride, so the rate constant for C-CI fission is more suppressed by non-adiabatic recrossing of the reaction barrier.In addition, C-C fission can proceed more adiabatically from the gauche conformer of chloroacetone than from near-planar geometries in acetyl chloride owing to a conformation dependence of non-adiabatic recrossing near the conical intersection. A final measurement of the conformation population dependence of the branching investigates the second contributing factor. 1. Introduction Much of our predictive ability for the branching between chemical reaction pathways has relied on statistical transition-state theories'-3 or, in smaller systems, quantum scattering calculations4 on a single adiabatic potential-energy surface.The potential-energy surface gives the energetic bar- riers to each chemical reaction and allows prediction of the reaction rates. Yet the chemical reaction dynamics evolves on a single potential-energy surface only if the Born-Oppenheimer' separation of nuclear and electronic motion is valid. Thus, the adiabatic approximation, though challenged at the inception of transition-state theory,? is often now implicitly assumed to be valid for bimolecular and unimolecular reactions in the ground electronic ~tate.~9~ Its shortcomings are only widely recognized for ion-molecule, charge tran~fer,~ and other reactions involving obvious elec- tronic curve The experiments presented here demonstrate the importance of considering the possibility of non-adiabaticity at the transition state of any chemical reac- tion with a barrier along the reaction coordinate, including ground-state bimolecular reactions, and identify two classes of chemical reactions in which non-adiabatic effects are criti- cal.t The adiabatic assumption was briefly discussed in ref. qa) and challenged by E. Rabinowitch in the discussion of the paper by Evans and Polanyi.6b The following paper6c also discussed the adia- batic assumption. 2. Reduction in Rate Constant from Non-adiabatic Recrossing of the Barrier Recent has shown that the breakdown of the Born-Oppenheimer approximation at a reaction barrier formed from an avoided electronic configuration cro~singl~*'~can dramatically reduce the rate constant for the chemical reaction and change the resulting branching between energetically allowed product channels. The qualit- ative mechanism for a reduction in the reaction rate due to non-adiabatic recrossing of the barrier is illustrated in Fig.1 for an A-B bond fission reaction with a barrier along the forward and reverse reaction coordinates. Along the adia- batic reaction coordinate the dominant electronic configu- ration changes from one bonding in the A-B bond, on the reactant side of the barrier, to one repulsive in the A-B bond, after the barrier in the exit-channel region. The change in electronic wavefunction required to follow the adiabatic reaction coordinate near the barrier is considerable and can result in a failure of the Born-Oppenheimer approximation.If the splitting between the adiabatic electronic surfaces at the barrier along the reaction coordinate is small,' 'reflecting the weak configuration interaction between the bonding and repulsive electronic configurations, the molecule may not tra- verse the barrier adiabatically. Instead the electronic wave- function may retain the bonding configuration character, resulting in a non-adiabatic hop to the upper bond potential- energy surface at the avoided crossing. The molecule feels the bound wall of that potential instead of undergoing bond fission on the lower adiabat.J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 8-1bonding configuration which result in the splitting between the adiabats at the -repulsive configuration Imixed character reaction coordinate Fig. 1 Schematic reaction coordinate for the A-BC --* A + BC reaction with a barrier to both the forward and reverse reaction. Along the lower adiabat, the dominant electronic configuration of the electronic wavefunction changes from bonding in character on the reactant side to repulsive (antibonding) in character on the product side. The figure also shows the upper bound adiabat formed from the avoided electronic crossing of the bonding and repulsive electronic configurations. If the Born-Oppenheimer approximation fails, the molecule retains its initial bonding electronic character at the barrier and makes a non-adiabatic 'hop' to the upper adiabat instead of proceeding to products on the lower adiabat.Figure repro- duced from ref. 12. Several classes of reactions are susceptible to a reduction in the rate constant due to non-adiabatic recrossing of the reaction barrier. A completely analogous mechanism to that described above results in a non-adiabatic reduction in the rate constant for electron-transfer reaction^.^ In a statistical expression for the reaction rate constant k = K(k, T/h)exp(-EJk, T) one may correct for this rec-barrier to C-Br fission. We end by qualitatively outlining a simple molecular orbital picture for why this splitting is expected to be anomalously small for Woodward-Hoffmann- forbidden reactions, making these reactions so susceptible to a non-adiabatic reduction in reaction rate.Indeed, although the barrier is often cited as the reason why this class of reac- tions is unfavourable, the present results show that non-adiabatic recrossing may be the dominant reason why these reactions are 'forbidden'. Non-adiabaticityin Product Branching in Br(CH,),COCI The first result of our experiments on the competition between photodissociation pathways in bromoacetyl and bromopropionyl chloride showed that the reaction channeI with the lowest energetic barrier need not be the major one; it can be so suppressed by non-adiabatic recrossing that a reaction channel with a much higher barrier can dominate.Excitation of BrCH,COCl to the lowest 'A" potential-energy surface via the '[n(O), n*(C=O)] transition at 248 nm results in a competition between C-Br and C-C1 fission, with a minor contribution from C-C fission." Although sta-tistical transition-state theories predict that, given compara- ble pre-exponential factors, the reaction pathway with the lowest energetic barrier, C-Br fission, should dominate, the experiments find the C-Cl bond cleaves preferentially by a ratio of C-C1 :C-Br = 1 : 0.4 in bromoacetyl chloride upon excitation of the '[n(O), n*(C=O)] transition.7 (The analysis requires separate identification of the C-Br fission resulting from the '[n(O), n*(C=O)] transition us. C-Br fission resulting from excitation of an overlapping electronic transition; this is described in the next paragraph.) Fig.2 shows the time of flight from the photolysis region to the electron-bombardment ionization detector of the primary photofragments as measured with a molecular beam tech- nique described in Section 5. The model developed to explain rossing with (Traditionally," however, a reduced K has been used to correct for recrossing due to a large curvature of the potential-energy surface in the transition state region, not for recrossing due to non-adiabatic transitions.) S,2 reactions could also evidence a non-adiabatic reduction in the rate con- stant,'* because again the barrier is formed from an avoided electronic curve crossing,' but this possibility has not been closely investigated.The work reviewed in the next two sec- tions shows that the reduction in rate due to non-adiabatic recrossing of the barrier markedly changes the branching between competing bond fission pathways belonging to two classes of reactions in which the splitting between adiabats is anomalously small, Woodward-Hoffmann-forbidden reactions"." and reactions with a conical intersection" along the reaction coordinate. 3. The Importance of Non-adiabatic Recrossing in Woodward-Hoffmann-for bidden Reactions : Br(CH,),COCl The experiments described in this section on the photoin- duced Woodward-Hoffmann-forbidden bond cleavage reac- tions of Br(CH,),COCl focus on how non-adiabatic recrossing of the low-energy barrier to C-Br fission barrier markedly decreases the branching to C-Br fission from that predicted with adiabatic transition-state theories.''*" They further investigate the intramolecular distance dependence of the electronic configuration interaction matrix elements a transmission factor K of less than 0116.~'~~ the experimental results attributed the reduction in branching to C-Br fission on the 'A surface to non-adiabatic re-crossing of the barrier to C-Br fission. Fig. 3 shows that if the molecule retains the non:=o bonding configuration as it approaches the barrier to C-Br fission, it hops to the upper potential-energy surface at the avoided crossing and turns back towards the Franck-Condon region instead of pro- ceeding over the barrier to C-Br fission along the lower adiabatic reaction coordinate.The experiments on bromo- propionyl chloride described next test this model's predic-tions. The experiments on bromopropionyl chloride were initiated to test whether we could further suppress the branching to C-Br fission by choosing a system where the splitting at the avoided crossing which forms the barrier to C-Br fission would be significantly reduced from that in bromoacetyl chlo- ride. This smaller splitting would enhance the probability of the barrier being non-adiabatically recrossed, further decreasing the rate constant for C-Br fission (see schematic reaction coordinate in Fig. 3). Because the barrier results from the avoided crossing of the no n&o and the npBr o&,, configurations, the additional intervening CH, group between the C=O and C-Br orbitals would necessarily reduce the electronic interaction matrix elements between t Identification of the small fraction of C-C fission in bromo-acetyl chloride by using a comparison with bromoacetone allowed a better determination of the C-Br branching.See analysis in ref, 12. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 1.o 0.8 0.6 0.4 0.2 0 1.o 0.8 0.6 0.4 0.2 0 100 200 300 400 500 600 700 800 time-of-arrival/ps Fig. 2 Laboratory time-of-flight data, from ref. 10, of the photofrag- ments detected at (a) 79Br+ and (b) 35Cl+ from bromoacetyl chloride photodissociated at 248 nm with an unpolarized laser.The fits to the individual contributions from C-C and C-Br fission are described in and taken from ref. 1Oc. The forward convolution fit to the signal at Br' assigned to Br atoms, which dominates the fast side and peak of the spectrum, was obtained with the P(E,) for C-Br fission, shown in Fig. 5 (a). these two configurations, resulting in a smaller splitting between the adiabats at the barrier. The experiments showed that while in bromoacetyl chloride, the initial '[n(O), n*(C=O)] electronic transition resulted in a C-Cl :C-Br bond fission ratio of 1.0 : 0.4, in bromopropionyl chloride the same initial transition resulted in a C-Cl : C-Br bond fission ratio of 1.0 : <0.05.'0'*' ' The <0.05 branching to C-Br fission represents an upper limit; in fact, a comparison of the distributions of relative kinetic energies imparted to the C-Br fission fragments in the two molecules determined from the data in Fig.2 and 4 show that essentially all of the Br-atom products observed from bromopropionyl chloride merely result from an overlapping transition to an electronic state diabatically repulsive in the C-Br bond. Fig. 5 com-pares the kinetic energy distribution of the C-Br fission fragments from bromoacetyl chloride, upper frame, which evidences C-Br fission from both the '[n(O), n*(C=O)] transition and from the overlapping repulsive transition, with that from bromopropionyl chloride, lower frame. When you superimpose the component from bromoacetyl chloride for C-Br fission from just the overlapping transition, it corre- sponds closely to the entire distribution from bromo-propionyl chloride as shown in Fig.5. Thus, the lower-energy component from [n(O), n*(C=O)] excitation is absent in bromopropionyl chloride; the higher-energy C-Cl fission channel completely dominates C-Br fission on the 'A'' surface despite being the channel with the higher barrier. This further dramatic reduction in branching to C-Br fission upon '[n(O), n*(C=O)] excitation supports the hypothesis BrCH2COCI BrCH,COCI C-Br -reaction coordinate -C-CI fission fission Fig. 3 Schematic reaction coordinates for C-Cl and C-Br bond fission from the 248 nm photodissociation of bromoacetyl chloride. The upper frame shows only the lowest 'A adiabatic excited elec- tronic surface where the barrier to C-Br bond fission is lower than the barrier to C-CI bond fission. Considering only this lowest adiabat leads to the incorrect prediction that C-Br bond fission should dominate in bromoacetyl chloride.The lower frame shows this lowest 'A" adiabat along with the upper 'A adiabat formed from the avoided electronic configuration crossing at the barriers to C-Cl and C-Br bond fission. In addition, the dotted lines in the lower frames show the diabatic electronic states. Preferential C-Cl bond fission in bromoacetyl chloride results because the greater coupling V,, between the n0n,*=, and the n,,a,*<, states allows the molecules to switch from one configuration to the other, resulting in adiabatic crossing of the bamer to C-CI bond fission. The smaller coupling V,, between the n0n,*=, and the nBra&Br states results in trajectories retaining the no x2.=o configuration by making a non- adiabatic 'hop' at the avoided crossing which forms the barrier to C-Br fission, so more trajectories turn back from the repulsive wall on the bound surface, reducing the branching to C- Br fission.Adapted from ref. 11 that the additional intervening CH, spacer would decrease the splitting between the adiabats at the avoided crossing and thus increase the non-adiabatic recrossing of the reaction barrier. A single reference configuration interaction (single excitations only) calculation of the splitting between the adia- bats at the barrier to C-Br fission in these two systems further tests this conclusion.While the approximations inher- ent in the method and the minimal (STO-3G*) basis set pre- clude quantitative accuracy, the results given in Fig. 6 and Table 1 show that the splitting at the avoided crossing is an order of magnitude smaller in bromopropionyl chloride than in bromoacetyl chloride," consistent with the interpretation of the experimental results. The splitting in both systems is so small that a simple Landau-Zener calculation shows that fewer than 5% of the reactive events that would lead to C-Br bond fission on the adiabatic potential surface h c'c 0.8 0.6 b - a CI 0.4 - 0.2 - 0-h 0.8.-$ C 3 4 0.6 -U -0.4 v 2 0.2 -0-100 200 300 400 500 600 time of arrival/ps Fig. 4 Laboratory time-of-flight data, from ref.11, of the photofrag- ments of bromopropionyl chloride detected at C1' (a) and Br+ (b)at 248 nm with an unpolarized laser. The source angle was 20" in (a) and 10" in (b). The forward convolution fit to the portion of the signal at Br+ assigned to Br atoms was obtained with the P(E,) for C-Br fission in Fig. 5 (b). actually cross the barrier adiabatically.? The other 95% (or more in bromopropionyl chloride) retain the n,n.,*=, con-figuration at the avoided crossing and hop to the upper adiabat, resulting in the trajectories turning back toward the reactant region. With a factor of ten smaller splitting in bromopropionyl chloride compared to bromoacetyl chloride, the diabatic recrossing increases by a factor of 100, consistent with the experimentally observed loss of all C-Br fission upon '[n(O), n*(C=O)] excitation.Thus the calculations and experiments on bromopropionyl chloride, designed to test experimentally the intramolecular distance dependence of the splitting and the resulting non-adiabatic recrossing of the barrier to C-Br fission, confirm that the additional inter- ? Because the barrier to the reaction is not accurately determined by the simple ab initio calculations done on this system, and because the splitting, and thus the non-adiabatic recrossing probability, varies along the seam of the avoided crossing, we cannot give an accurate estimate of the recrossing probability.We obtained a rough estimate from a one-dimensional Landau-Zener formula with the following approximations: (1)the velocity through the avoided crossing was. estimated by assuming 10 kcal mol-' total internal vibrational energy in the molecule at the bamer to C-Br fission with 1/(3N -6) of the energy in the reaction coordinate, the reduced mass was taken as between the C and the Br atoms, the difference in slopes of the two surfaces in a diabatic representation was taken by extrapolating through our calculated adiabats at the avoided crossing and was close to 56 x lo3 an-' A-', and the offdiagonal potential coupling was taken as half the splitting in a cut through the seam where the splitting was 22.6 cm-' for bromopropionyl chloride and 225 an-' for bromoacetyl chloride.This estimate gave Phop= 0.9995 for bromopropionyl chloride and 0.964 for bromoacetyl chloride, so a negligible fraction of the trajectories follow the adiabatic reaction coordinate on each crossing attempt for bromopropionyl chloride. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 nI-a'u,Q 401: O0 100 1 nI-'u,k 0 5 10 15 20 25 30 35 40 E,/kcal rnol-' Fig. 5 Centre-of-mass product translational energy distributions, P(E,)s from ref. 11 and 12,for the C-Br fission channel in bromo- acetyl chloride (a)and bromopropionyl chloride (b)at 248 nm. C-Br fission from the '[n(O), n*(C=O)] excitation is identified by compar- ing it to kinetic energies imparted in C-Br fission in a molecule in which the repulsive electronic transition does not overlap the '[n(O), n*(C=O)] transition to the 'Affpotentialenergy surface of interest.Note that the P(E,) for bromopropionyl chloride, shown in solid circles in the bottom frame, corresponds almost exactly to a P(E,) characteristic of dissociation upon excitation of the overlapping [n,(Br), o*(C-Br)] transition (squares) with minimal or no contribu- tion from the overlapping [n(O), n*(C=O)] transition. vening bond further suppresses C-Br fission by at least an order of magnitude. The next section outlines why Woodward-Hoffmann forbidden reactions are particularly susceptible to a reduction in reaction rate constant from non- adiabatic recrossing of the reaction barrier.Identifying Woodward-Hoftinann-forbidden Reactions as a Class Subject to Non-adiabatic Recrossing In the class of reactions designated as Woodward-Hoffmann forbidden, individual electronic orbital symmetry is not con- served along the reaction ~oordinate,'~*'~ and the barrier resulting from the avoided crossing is often cited as the reason why these reactions are unfavourable. However, the experiments and calculations on the Woodward-Hoffmann- forbidden excited-state C-Br bond fission reaction showed that the reaction was not disfavoured due to a higher energy barrier than the competing reaction pathway, it was 'forbidden' because of a very high non-adiabatic recrossing probability. The nuclear dynamics unexpectedly turn back from the avoided crossing region at energies well above the barrier, markedly reducing the reaction rate constant. We argue here that this class of reactions should show anom- alously small splittings at the avoided crossing which forms the reaction barrier, so non-adiabatic recrossing of the reac- tion barrier may be the dominant reason why Woodward- Hoffman-forbidden reactions are unfavourable.J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 47000 bromoacetyl chloride barrier to C-Br fission I I 1 . 51600 brornoacetyl chloride barrier to C-CI fission K I I brornopropionyl chloride barrier to C-Br fission 48000 b I 1 II '. 52000 -bromopropionyl chloride barrier to C-CI fission 7 \ / 46600 5 51600 * I E 46200 * >512008 2 V,, = 404 crn-' 0 I I 1 I\454OOL/ I 50000' ' 46400 50400 I-_ 2.350 2.335 2.320 2.305 2.290 2.200 2.215 2.230 2.245 2.260 2.370 2.355 2.340 2.325 2.310 2.510 2.225 2.240 2.255 2.270 R( C-&)/A R(C-CI)/A R( C-Br) /A R(C-Cl)/A 70000 I I I I 1 I 1 La1 *.-a60000 /* I"'. /' / ., '. /* ,/* /----2----1dId P5 30000 * -30000-Q) 20000 ' 20000 . Fig. 6 Cuts, from ref. 11, through the calculated ab initio electronic surfaces for bromoacetyl chloride with R(C-0) = 1.188 A (left) and bromopropionyl chloride with R(C-0) = 1.295 8, (right). The boxed-in portions at the barrier to each bond fission pathway, which are enlarged in the insets above each, show that the probability of C-Br bond fission decreases in bromopropionyl chloride because the splitting between adiabats at the barrier to C-Br bond fission decreases by a factor of ten from that in bromoacetyl chloride.The smaller adiabatic splitting at the barrier to C-Br bond fission in bromopropionyl chloride results in a higher probability of non-adiabatic recrossing of the barrier and suppression of C-Br bond fission. For the particular cut along the avoided crossing seam shown here, the splitting at the avoided crossing to C-Br fission reduces from 225 cm-' in bromoacetyl chloride to 22 cm-' in bromopropionyl chloride. Other cuts are given in Table 1. To argue qualitatively why this class of reactions should product side of the barrier, (. * (n.J'(n,)z(n~=o)o(o~x)l}, by show anomalously small splittings at the reaction barriers, we two electrons.Configuration interaction matrix elements mix consider a comparison between reactions which have a and split these two electronic configurations at the avoided barrier formed from an avoided crossing between electronic crossing which forms the barrier to C-X bond fission. In configurations where both individual orbital symmetries and this two-state model, with no orthogonality assumed between overall electronic state symmetry is conserved, us. ones where reactant and product molecular orbitals or between YRand overall symmetry is conserved but individual orbital sym- Yp,the general expression for the splitting between the adia- metry is not. The argument closely follows that of Silver,I4 batic Born-Oppenheimer potential-energy surfaces who was trying to address the idea of 'barrier energy splitting = 2(8 -aSK1 -S2)-' (1)lowering' from the non-adiabatic crossing energy for these two classes of reactions.Although we retain much of his in which a is the energy at which the diabats cross, S is the argument (the splitting between adiabats is twice the 'barrier overlap integral (YRIYp)/Cand B is the interaction, reson- energy lowering'), we emphasize that the critical point here is ance, or exchange energy (YRl~l~p)/C;C corrects for that the height of the barrier, on which Silver focused, is not unnormalized wavefunctions. However, for Woodward-as important for these systems as the probability of crossing Hoffmann-forbidden reactions, like C-Cl and C-Br bond the barrier adiabatically.fission on the lowest 'A" electronic state of bromoacetyl and Using the Woodward-Hoffmann-forbidden reaction bromopropionyl chloride, the overlap integral S is zero described in the section above as an example, consider the because individual orbital symmetry is not conserved. In dominant electronic configuration contributing to the elec- planar C, conformers of bromoacetyl and bromopropionyl tronic wavefunction, VR,on the reactant side of the barrier, chloride, the n:=o orbital has a" symmetry while the represented by one electron in an no orbital and another in a orbital has a' symmetry so the overlap integral n& orbital, and the dominant configuration contributing to ~~ the electronic wavefunction, Yp, on the product side of the 7 The expression for the energy lowering AE from the diabatic barrier, represented by one electron in an n, orbital and one crossing energy given in eqn.(15) in ref. 14 is incorrect, but the in a o& orbital (where X-Cl or Br). The reactant configu- correct expression, also given in footnote 20 in ref. 7, may be easily differs from that on the derived from eqn. (9) in ref. 14.ration, {---(n.J2(no)1(7r~=o)1(a&Jo), J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 1 Summary of ab initio calculations of the splitting between adiabats at the barriers along the C-Cl and C-Br bond fission reaction coordinates, at a variety of C-0 bond lengths, in bromoacetyl and bromopropionyl chloride R(C=OJA R(C-B,dA 1.1881.313 1.935 1.935 1.3881.588 1.935 1.935 R(C= oJA R(C-Br) at barrier/A 1.188 2.3205 1.313 2.522 1.388 2.627 1.588 2.777 ~~ R,c=oJA R(~-~~JA 1.195 1.935 1.295 1.935 1.395 1.935 1.495 1.935 ~ R,c =OJA R(C-Br) at barrier/A 1.195 2.3439 1.295 2.503 1.395 2.626 1.495 2.7247 Bromoacetyl chloride Barrier to C-Cl bond fission energy/cm-' at barrier on 'A, referenced to minimum Ro,, at barrierldi in the ground state 2V',/Cm -1 2.232 50548 401.7 2.382 44 192 88.7 2.464 44763 57.3 2.553 53 264 1 160.0 Barrier to C-Br bond fission energy/cm-' at barrier on 'A, referenced to minimum RoIJA in the ground state 2Vl Jcm -1.789 46 136 225.0 1.789 40051 137.9 1.789 40 821 121.0 1.789 50 513 67.8 Bromopropionyl chloride Barrier to C-Cl bond fission energy/cm-' at barrier on 'A", Ro,, at barrier/A 2.239 2.351 2.453 2.523 Barrier to C-Br bond fission R(C4lJA 1.797 1.797 1.797 1.797 referenced to minimum in the ground state 2 Vl Jcm - 50 897 404.1 45 335 130.6 45 296 106.5 48 279 494.4 energy/cm-' at barrier on 'A", referenced to minimum in the ground state 2V1&rn -' 47 536 22.6 41 698 20.2 41 324 12.1 44550 9.7 The first three columns show the C-0, C-Br and C-Cl bond lengths, in A, at the barrier.The fourth column shows the calculated energy of the lowest 'A" adiabatic electronic surface at the barrier, while the fifth column, labelled 2V12, shows the splitting between the two lowest 'A" states at the barrier.Table from ref. 11. (xZ=~CJZ-~)= <a" I a') = 0. Similarly, the n, orbital has a'' symmetry while the no orbital has a' symmetry so the overlap integral (n, I no) = (a" 1 a') = 0. Because individual orbital symmetry is not conserved for Woodward-Hoffmann-forbidden reactions, all one-electron integrals that contribute to the resonance and exchange energy represented by /? above are also zero, leaving only two-electron integrals to mix and split the electronic states at the avoided cro~sing.'~ splitting in W-H-forbidden reactions = 2P2 (2) Thus the splitting between the adiabats at the barrier is expected to be anomalously small for this class of reactions. Indeed, our simple electronic structure calculations show the splitting is on the order of hundreds of wavenumbers for both C-Br and C-CI fission in bromoacetyl chloride and on the order of only tens of wavenumbers for C-Br fission in bromopropionyl chloride.In addition, there is preliminary computational evidence that upon breaking the symmetry element that makes the reaction Woodward-Hoffmann-forbidden, as in the gauche conformer of these molecules or of bromoacetone' (see Table 2, later), the splitting increases considerably. The marked intramolecular distance dependence of the splitting and resulting non-adiabatic recrossing probability for C-Br fission in Br(CH,),COCl can also be understood by analysing the configuration interaction matrix elements (equal to twice the off-diagonal potential coupling between two diabatic electronic configurations in the diabatic representation) using an orthogonal basis set.For singlets, they are:15b The first matrix element, similar to that in a Forster model for intramolecular electronic energy transfer, decreases with the separation between chromophores due to the r12 in the denominator, while the second matrix element, similar to that in the Dexter energy-transfer mechanism, decreases roughly exponentially as the overlap densities no(l)nx(l) and n,*,0(2)acx(2) decrease. The reason for the parallel with energy-transfer theory is the implicit intramolecular elec- tronic energy transfer required along the adiabatic reaction coordinate for this system.To proceed over the barrier to J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 C-Br fission on the A" potential-energy surface, the elec- tronic wavefunction must change from no .nz=o in character to npBr in character at the avoided crossing which forms t~,?~~ the barrier to C-Br fission. If the off-diagonal potential coupling between these two non-adiabatic electronic configu- rations is small (due in part to the spatial separation between the C=O and C-Br orbitals), the electronic wavefunction can retain n7r,?j=o character as the molecule approaches the barrier to C-Br fission. Then, instead of going over the barrier on the adiabatic potential-energy surface it turns back from the attractive potential of the nnz=o diabat shown by the dotted line in Fig.3, resulting in a smaller branching to C-Br fission than expected, as observed in the experiment. (This is equivalent to non-adiabatically hopping up to the upper adiabat, reversing direction on the attractive wall, and returning to the reactant upon non-adiabatic transition to the lower adiabat.) Indeed, electron-transfer reactions and intramolecular electronic energy-transfer processes are often described in a diabatic representation, where the rate is pro- portional to the square of the off-diagonal potential coupling matrix element ; the larger the off-diagonal potential coupling between diabats, the larger the splitting and thus the higher the probability of following the adiabatic electron-transfer reaction coordinate and the faster the electron-transfer rate.7 transfer rate.' 4.Conformation Dependence of Non-adiabatic Recrossing near a Conical Intersection: C-C fission in CH,COCH,Br The importance of non-adiabatic effects at a conical intersec- tion has long been recogni~ed.'~?' 5,20 In condensed-phase photochemical processes where internal energy can be drained from the local system, they have been termed funnels, providing a region of an excited potential-energy surface where transition to the ground state can occur with high probability.'5 The experiments on the competition between C-Br and C-C photocleavage in anti-and gauche-bromoacetone described below ', elucidate two general fea- tures of reactions which must proceed past a conical intersection along either an excited-state or a ground-state adiabatic reaction coordinate (see schematic excited-state reaction coordinate for C-C fission in bromoacetone in Fig.7), their dramatic conformation dependence and their essen- tial non-adiabatic character. We end with outlining why many reactions which are described as 'symmetry forbidden' are in fact symmetry forbidden only at a singularity on the multidimensional reactive potential-energy surface, so they are better described as forbidden due to the high non-adiabatic recrossing probabiity in the region of the conical intersection. The study of bromoacetone'2 was initiated to investigate the conformation dependence of the non-adiabatic recrossing probability along the C-Br bond fission reaction coordinate, only to find that the conformation dependence of C-C fission through a conical intersection dominated the differ- ence in branching.? This paragraph outlines the three initial observations which led us to turn to considering the confor- mation dependence of C-C fission through a conical inter- section: (1) in a thermal population of bromoacetone -f The bromoacetone and chloroacetone conformer which we refer to here as 'trans' or 'anti' should, in correct nomenclature, be called s-cis, as the dihedral angle between the C-CI(Br) and the C=O bond is zero and the C1 or Br and 0 atoms, having the highest atomic numbers, should determine the groups to which the geometry refers.However, we retain the non-standard name of trans for this conformer in order to remain consistent with several earlier studies.% 5a Fig. 7 Schematic excited-state reaction coordinate for C-C bond fission in bromoacetone (top). The cross-sections show the different regions of the conical intersection along the C-C fission reaction coordinate sampled by dissociating the anti us. the gauche conformer. The frames on the r.h.s. of the figure show three slices through the conical intersection: the lowest at planar geometry (atorsion= 0);the middle at close to planar geometries (small a) where the adiabats are weakly split, so non-adiabatic recrossing dominates the dynamics; and the uppermost at highly non-planar geometries, sampled by dis-sociative trajectories from the gauche conformer, where the adiabats are strongly split so C-C fission can proceed adiabatically.Adapted from ref. 12. conformers, both C-C and C-Br fission occur; (2) the angular distribution of Br atoms shows C-Br fission occurs primarily from the minor anti conformer, not the dominant gauche one; and (3) low-level ab initio calculations show C-Br fission is more, not less, non-adiabatically suppressed in the anti conformer than in the gauche, so the conformation dependence of the C-C : C-Br branching ratio is not deter- mined by the C-Br fission reaction coordinate; it must reflect the conformation dependence of C-C fission. The photofragment time-of-flight spectra in Fig. 8 show the first result: photoexcitation of bromoacetone at 308 nm in the nnz,o absorption band, analogous to the absorption excited in bromoacetyl chloride above without the overlapping repulsive transition, results in both primary C-Br and primary C-C bond fission products.Linear momentum con- servation allows us to use the velocities of the Br atoms detected in the Br+ spectrum to identify the portion of the CH,CO+ spectrum in Fig. 8 (b) from the momentum-matched CH,COCH3 photoproduct cracking to CH,CO + in the mass spectrometer. The remaining signal in that spectrum is easily assigned to COCH, from primary C-C bond fission, as the COCH, product is also seen with the same distribution of arrival times, peaking near 340 ps, at the CH,CO+ parent ion and as this portion of the distribution is momentum-matched to a weak signal at CH,Br+ from CH,Br product.Armed with the knowledge that C-C and C-Br fission compete upon excitation at 308 nm, the angular distribution of the Br gave the second key result, our first probe of a conformation dependence to the branching. If there were no conformation dependence to the branching, the angular distribution of the Br atom fragments would be a 1588 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 2 Summary of ab initio calculations of the splitting between adiabats at the barrier to C-Br bond fission in anti-and gauche-bromoacetone anti-Bromoacetone Barrier to C-Br bond fission ~~~ energy/cm-' at barrier on 1 'A, R, =oJA R(C-Br) at barrier/A referenced to minimum in the ground state 2Vl Jcm -1.182 2.39 51 131 129 1.282 2.53 44 008 97 1.392 2.67 42 941 75 1.492 2.77 46 503 59 gauche-Bromoacetone Barrier to C-Br bond fission energy/cm-' at barrier on first excited singlet, R{c=oJA R(C-Br) at barrier/A referenced to minimum in the ground state 2v,,/cm-1 1.186 2.51 45 808 1982 1.280 2.66 39 143 1220 1.380 2.83 37 645 720 1.480 3.00 39 324 432 The first two columns gve the C-0 and C-Br bond lengths, in A, at the barrier.The third column shows the calculated energy at the barrier of the lowest (of A" symmetry for the anti conformer) singlet excited adiabatic electronic surface (referenced to the minimum energy in the ground state). The fourth column, labeled 2V1, ,shows the splitting between the two adiabats at the barrier formed from the avoided electronic curve crossing.Only the C-Br bond length was varied to find the avoided crossing; the C=O bond lengths are listed in column 1, all other internuclear geometries are frozen at the equilibrium geometry given in ref. 26. Table from ref. 12. weighted average of the angular distribution from each con- 1.o former. Assuming a thermal population of gauche-and anti-bromoacetone at the nozzle temperature of 180°C (the 0.8 supersonic expansion in helium is a weak one, so while the 0.6 relative translational and rotational energies are effectively cooled, the conformer populations are not2') the predicted? 0.4 anisotropy of the Br atoms is = 22.2%(8,,,,) 0.2 + 77.8%(8g,,h,) = 22.2%(1.15) + 77.8%( -0.75) = -0.33 if the branching ratio between C-C and C-Br fission is the 0 same for both conformers.However, the angular distribution of the Br atoms shown in Fig. 9 evidences a much more parallel angular distribution of the photofragments than that calculated; clearly, the gauche and anti conformers do not contribute at all equally to C-Br fission. Having been fitted by an anisotropy parameter of B = 0.8, the angular distribu- tion shows that C-Br fission results from the anti conformer. In the limiting case, to be consistent with the measured anisotropy at most 18% of the C-Br bond fission events result from gauche bromoacetone even though 78% of the molecules are in the gauche conformer. Thus, although we observe both C-C and C-Br fission in bromoacetone, it is apparent that C-Br fission can dominate C-C fission in the anti conformer, but not in the gauche.Although one might try to understand this based on the conformation dependence of the non-adiabatic recrossing of the barrier to C-Br fission, the final result, a computational one given in Table 2, showed the splitting between the adiabats at the barrier to C-Br fission is much larger in the gauche conformer than in the anti and the barrier heights are comparable. (Although a preliminary result, this difference in the splitting is consistent with the fact that in the gauche conformer the reaction is no longer strictly Woodward-Hoffman forbidden.) Thus non- 100 200 300 400 500 600 700 time of arrival/ps t To predict Bmri and #lglruchein the axial recoil limit, we use the Fig.8 Laboratory time-of-flight data, from ref. 12, of the photofrag- expression #I2P,(cos a) given in ref. 22(a), (b) and the calculated = ments of bromoacetone detected at "Br+ (a), CH,CO+ (b) and equilibrium geometries in ref. 22(c). We assume that the dissociation CH,CO+ (c) at 308 nm with an unpolarized laser. The portions of quantum yield and absorption spectrum are insensitive to conformer each spectrum assigned to primary C-C and C-Br bond fission are at this wavelength; the temperature dependence measurements identified in ref. 12. support this approximation. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 . . . , . . . I T . . . I . . . I . . . 9000 000 8500 mN 8000 t P UJ C 7500 t s 7000 W 6500 0 40 80 120 160 200 laboratory polarization angle/degrees Fig.9 Laboratory angular distributions of the Br+ signal which results from primary C-Br bond fission in bromoacetone photo- dissociated at 308 nm with linearly polarized light. @ is the angle of the laser electric vector with respect to the detector axis (measured in the opposite sense of rotation as the source angle). The data points represent the integrated experimental TUF signal measured at six different laser polarization angles. Line fits show the predicted change in detected scattered signal intensity with laser polarization angle obtained, after transformation from the centre-of-mass to laboratory frame, with three trial anisotropy parameters, j= 1.0,fi = 0.8 and /?= 0.6.Adapted from ref. 12. adiabatic recrossing of the C-Br fission barrier should suppress C-Br fission more effectively in the anti conformer, not in the gauche, yet the angular distribution shows C-Br fission occurs primarily from the anti. Clearly the conforma- tion dependence to the branching must result from a dra- matic conformation dependence along the C-C reaction coordinate; although C-Br fission could occur as easily in the gauche as in the anti, C-C fission must overwhelm it in the gauche conformer. The most compelling model for why C-Br fission domi- nates C-C fission in the anti conformer but not in the gauche conformer comes from considering the C-C fission reaction coordinate.On the lowest singlet and the lowest triplet excited electronic states the reaction coordinate for C-C fission is formed from the avoided crossing of the Franck-Condon excited n0n,*=, state and a repulsive a& c~nfiguration.~~-~'tBecause the no n&o configuration has A" symmetry in C, while the repulsive a& state has A' symmetry, the two configuration states interact only at non- planart geometries, resulting in a conical intersection along the C-C fission reaction coordinate as depicted schemati- cally in Fig. 7. The electronic configuration interaction matrix elements which contribute to V,, and couple the n,n&o and aa& configurations are necessarily zero in C, symmetry. Likewise, the splitting between the upper and lower adiabats in regions of phase space near the conical intersection is quite small, so any dissociative trajectories which attempt to traverse the conical intersection along the 7 Although a-cleavage is usually assumed to occur via internal conversion or intersystem crossing, an excited-state singlet mecha- nism has been reported in ref.25 and we note that the 'A, 'm, asymptotic limit of the ground state must have a corresponding anti- bonding 'OQ* state that should correlate adiabatically with the lowest 'A,h*, state in geometries where the plane of symmetry is broken. 1We use the words planar and non-planar here to refer to molec- ular geometries that do or do not have a plane of symmetry. Of course, although all the heavy atoms are in a plane in 'planar' geometries, the H atoms are not. 1589 adiabatic C-C fission reaction coordinate in regions of phase space close to planar geometries will not be able to dissociate, but will rather retain bound no .~l& electronic character and return to the Franck-Condon region.It is these geometries that are accessed when one photodissociates the anti conformer, so non-adiabatic recrossing of the C-C fission reaction barrier near the conical intersection, then, provides the best explanation for why C-C fission cannot compete effectively with C-Br fission in the anti conformer. Conversely, photodissociation of the gauche conformer allows Franck-Condon access to dissociative wavefunctions that traverse the conical intersection at non-planar geo-metries where the adiabats avoid each other strongly, so C-C fission can proceed adiabatically (see Fig.7). The lack of observation of C-Br fission from the gauche conformer suggests that once C-C fission can proceed more adia-batically, it dominates C-Br fission. A final experimental measurement tests this model by changing the relative popu- lation of anti and gauche conformers in the beam and deter- mining how the observed branching ratio between C-C and C-Br fission changes. Fig. 10 shows that upon changing the nozzle temperature from 100 to 40O0C, and thus decreasing the fraction of molecules in the lower-energy gauche con-former, the branching ratio does indeed shift toward a smaller contribution from C-C fission.Although the percent contribution from each bond fission channel contributing to the CH,CO+ signal cannot give the absolute C-Br :C-C fission branching ratio at each conformational temperature because the daughter-ion cracking patterns of CH,COCH, and COCH, are unknown, we can obtain a precise measure of the relative branching ratio change and compare it directly to the relative change in conformer populations. Assuming no cooling of conformer populations in the expansion,21 the 1.2 1 .o h v)*.' 0.8.-C 0.6 0.4 0.2 0 ? 85% C-Br fission 15% C-C fission 100 200 300 400 500 600 700 time of arrival/ps Fig. 10 Laboratory time-of-flight spectra at two node tem-peratures of the photofragments detected at CH2CO+ from bromo- acetone photodissociated at 308 nm: (a)with a nozzle temperature of 100"C; (b) with a nozzle temperature of 400 "C.The source angle was 10" for both spectra. Adapted from ref. 12. relative change in conformer population in heating the nozzle from 100 to 400°C is: 400”~:( anti ) f C-Br) t 100°C: \4auchej,oo (0.34) (0.25) predicted = 1.4 (4) giving a predicted increase in the C-Br: C-C branching ratio of a factor of 1.4 if C-C fission dominates in the gauche conformer and C-Br fission dominates in the anti con-former. The experimentally observed change in branching ratio is quite similar: (z)observed = 1.6!(E) The result is in accord with the model presented in which dissociation from the anti conformer accesses regions of the C-C fission reaction coordinate near the conical intersec- tion, where it is non-adiabatically inhibited so cannot compete with C-Br fission, and dissociation from the gauche conformer proceeds through regions of the conical intersec- tion where the surfaces are further split from each other, so the C-C dissociation can proceed adiabatically and domi- nate C-Br fission.We have avoided using the terminology ‘symmetry forbidden’ when describing the lack of C-C fission from the anti conformer because, although commonly used, this lan- guage obscures the physical reason why a reaction pathway that traverses a conical intersection might be unfavourable. Indeed, the reaction is ‘symmetry forbidden’ only through a singular point on the potential-energy surface;t even small zero-point bending or torsional motion of the anti conformer at the transition state puts amplitude at molecular geometries where the adiabatic correlation goes smoothly from reactants to products.The reason why C-C fission in the anti con-former is suppressed is that trajectories that attempt to undergo C-C fission near, but not at, the point of conical intersection sample a region of phase space where the reac- tant and product electronic configurations are not strongly coupled, so the configuration interaction splitting between the upper and lower adiabats is small. Instead of following the adiabatic reaction coordinate, along which the electronic wavefunction changes from no ~rz=~to a& in character, the dissociative trajectory hops to the upper bound adiabat as it tries to traverse the C-C reaction barrier.Thus a reaction pathway through a conical intersection is not ‘symmetry forbidden’for most dissociative trajectories; rather, it is char- acterized by a high non-adiabatic recrossing probability. 5. Intramolecular Distance and Conformational Dependence of Non-adiabatic Recrossing: Competing C-C and C-Cl fission in CH,COCH,Cl YS.-CH,COCl The background work reviewed in the previous sections examined the competition between bond fission channels belonging to two classes of reactions highly susceptible to t If one only considers two internuclear degrees of freedom, one obtains a single point of conical intersection as shown in Fig.7. Of course, along any internuclear coordinate which does not break the plane of symmetry, this becomes a line of intersection. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 non-adiabatic effects, Woodward-Hoffmann-forbidden reac- tions and reactions proceeding through a conical intersection. Two key results in that work motivated the new experiments on chloroacetone presented below. The results on C-Br fission in bromopropionyl chloride, when compared with bromoacetyl chloride, showed that the additional intervening CH, spacer reduces the splitting between the adiabatic potential-energy surfaces at the barrier to C- Br fission, so non-adiabatic recrossing further supresses C- Br fission by over an order of magnitude.The experiments on bromo-acetone investigated the conformation dependence of non- adiabaticity at a conical intersection, supporting a model in which non-adiabatic recrossing of the barrier to C-C bond fission depends strongly on molecular conformer. While the anti conformer accesses regions of the conical intersection where the splitting between adiabats is very small, the gauche conformer accesses regions where C-C fission can proceed adiabatically and dominate C-Br fission. Those two results led us to predict that in chloroacetone C-C fission may effectively compete with C-Cl fission upon nn* excitation. Although previous work on a closely related system, acetyl chloride,26 showed that only primary C-Cl fission occurs, the increased distance between the C=O and C-Cl orbitals in chloroacetone should reduce the splitting at the avoided crossing which forms the barrier to C-Cl on the A potential-energy surface; the increase in non-adiabatic re-crossing of the barrier to C-Cl fission may allow C-C fission to compete.In addition, while acetyl chloride disso- ciates from near-planar geometries where C-C fission would be suppressed by non-adiabatic recrossing of the conical intersection, chloroacetone offers a gauche conformer from which the C-C channel could proceed more adiabatically. Thus both effects lead us to the prediction that C-C fission should compete effectively with C-Cl fission in chloroace- tone. The following experiments and calculations test this prediction.Experimental Method To measure the photofragment velocities and angular dis- tributions from the photodissociation of chloroacetone, ClCH,COCH, , we used a crossed laser-molecular beam apparat~s.~’*~*Upon photodissociation with a pulsed excimer laser, neutral dissociation products scatter from the crossing point of the laser and the molecular beam with velo- cities determined by the vector sum of the molecular beam velocity and the recoil velocity imparted in the dissociation. Those scattered into the acceptance angle of the differentially pumped detector travel 44.1 cm to an electron bombardment ionizer and are ionized by 200 eV electrons. After mass selec- tion with a quadrupole mass filter, the ions are counted with a Daly detector and multichannel scalar with respect to their time of flight (TOF)from the interaction region after the dis- sociating laser pulse.Upon subtraction of the calibrated ion flight time, forward convolution fitting of the TOF spectrum determines the distribution of energies released to relative product translation in the dissociation. The angular distribu- tion of the scattered photofragments is obtained with a lin- early polarized photolysis beam by measuring the variation in signal intensity with the direction of the electric vector of the laser in the molecular beam/detector scattering plane. The molecular beam was formed by expanding gaseous chloroacetone, at its vapour pressure at 45 “C, seeded in He to give a total stagnation pressure of 300 Torr.The 0.076mm diameter nozzle was heated to 200°C in the measurements to determine the angular distribution of the primary photofrag- ments. The peak beam velocity was 1.38 x lo5 cm s-l with a full-width-at-half-maximum of 18%. To determine the J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 changes in the relative branching between primary C-Cl and C-C bond fission as a function of the trans : gauche ratio in the parent molecular beam the data was retaken at two additional nozzle temperatures, 100°C and 400°C. To measure the velocity of the parent molecular beam in situ, the molecular beam source was rotated to point into the detector and a chopper wheel raised into the beam. To measure the velocities of the neutral photofragments, the molecular beam source is rotated to a different angle in the plane containing the beam and detector axis, a plane perpendicular to the laser beam propagation direction.Laser polarization angles and molecular beam source angles are given here with respect to the detector axis, the first defined as positive with clockwise rotation and the other as positive with counterclockwise rotation. Time-of-flight and angular distribution measurements were made on chloroacetone photofragments at 308 nm. The source angle was maintained at 15" with respect to the detec- tor axis for the data with the 200°C nozzle, and 10" for the data with the 100°C and 400°C nozzle. The unpolarized laser power from a Questek 2640 excimer was typically 130 mJ per pulse at 308 nm, with the light focused to a 5 mm2 spot size at the crossing region of the laser and molecular beam.Polarized spectra typically were taken at 30 mJ per pulse for 308 nm. Quadrupole resolution was adjusted to 0.9 u FWHM for m/z+ = 35 (Cl') and to 1.1 u for m/z+ = 49 (ClCH,), m/z+ = 43 (CH,CO+) and m/z+ = 42 (CH,CO+). For the anisotropy measurements, we disperse the unpo- larized laser light into two linearly polarized components with a single-crystal quartz Pellin-Broca and use the hori- zontal component, rotating the polarization into the desired direction with a half-wave retarder. The polarization depen- dent signal, integrated in many repeated short scans and alternating between each laser polarization direction, required no additional normalization to laser power or detec- tor efficiency.The strong signal observed at C1+ after 200000 shots evi- dences primary C-Cl fission. The momentum-matched CH,COCH, product was not detected at the parent ion after 200000 shots, but was observed in the strong signal for the CH,CO+ daughter ion after 400000 shots. The weaker signal at ClCHl after 700000 shots could be fitted entirely to ClCH2-COCH, fission. The energy distribution for this C-C fission also fit well to the slow shoulders in the signal at C1+ and CH,CO+. The weak signal at CH,CO+ after 400000 shots with a 100°C nozzle came largely from C-C fission, although the poor signal-to-noise allows for some contribution from the daughter ion of the CH,COCH, product from the C-Cl fission.At 200"C, after 500000 shots, the signal at CH,CO+ was even weaker, but showed a substantial contribution from C-C1 fission. No signal was seen after 300 OOO shots at 200 "C, at the mass corresponding to the ClCH,CO+ product of the other possible C-C fission channel, and the small signal after lo6 shots at the mass at 100°C is attributed to C-C1 and C-C fission from clusters formed in the expansion. Computational Method To help interpret the experimental results, we also present ab initio electronic structure calculations for acetyl chloride and chloroacetone using the GAUSSIAN 92 system of pro-gram~.~~We use second-order Msller-Plesset theory with full electron correlation and the 3-21G* basis set, with sym- metry constraints where appropriate, to obtain equilibrium geometries shown in Table 3 for chloroacetone (Fig.11) and Table 4 for acetyl chloride (Fig. 12); all other calculations use 1591 Table 3 Optimized ground-state geometries for trans-and gauche-chloroacetone parameter trans gauche r(c-Cl) 1.796 1.817 r(C1 -C2) 1.540 1.540 r(c2-c3) 1.531 1.523 r(C=O) 1.245 1.251 r(C--H,) 1.093 1.092 r(C--H,) 1.093 1.089 r(C-H3) 1.092 1.092 r(C--H,) 1.096 1.095 r(C-H,) 1.096 1.095 L(C-c-C1) 111.8 11 1.1 L(C,-C2==0) 123.4 120.1 L(C-c-C) 112.8 116.0 L(C-C-H 109.6 110.9 L(C-C-H,) 109.6 108.5 L(C- C- H3) 108.5 108.5 L(C-C-H4) 110.3 1 10.2 L(C-C-H,) 110.3 110.1 z(C1-c-c-0) 0.0 -123.4 z(c-c-c-0) 180.0 181.5 z(H -C-C=O) -120.1 117.5 z(H,-C-C=O) 120.1 -4.7 .t(H 3-C- C-0) 0.0 -2.2 z(H,-C-C=O) 120.1 118.2 z(H,-C-C=O) -120.1 -122.6 In the MP2(FULL)/3-21G* optimization the trans conformer was constrained to have a plane of symmetry.Bond lengths are given in 8, and bond angles in degrees. 011 Fig. 11 Chloroacetone. The torsional dihedral angle z[CIC(2)C(l) = 03 of 0" corresponds to the trans conformer.z4 the STO-3G* basis set. Configuration interaction with single and double excitations (CISD) calculations provide electronic ground-state energies in the harmonic region of the C-Cl and C-0 stretching potentials. These energies are then fit to Morse potentials with estimated dissociation energies of 83.5 Table 4 Optimized ground-state geometry for acetyl chloride r(c-CI) 1.822 1 4C-C) 1 S579 r(C=O) 1.2447 r(C-H,) 1.1044 r(C-H,) 1.1041 r(C--H,) 1.1041 L(C1-c=0) 120.5 L(C-c-0) 127.0 L(C-C-H 110.0 L(C-C-H2) 1 10.0 L(C- C- H 3) 110.0 z( c-c=0-a) 180.0 7(H ,-C-C=O) 0.0 r(H,-C-C=O) 120.0 z(H,-C-C=O) -120.0 In the MP2(FULL)/3-2AG* optimization the molecule was con-strained to have a plane of symmetry.Bond lengths are given in 8, and bond angles in degrees. 0 II Fig. 12 Acetyl chloride and 169 kcal mol-', respectively.? The ground state energy, as a function of the C-Cl and C=O stretching coordinates, is then assumed to be a sum of the two independent Morse potentials. Configuration interaction with single excitations (CIS) calculations provide excitation energies from the ground electronic state to the relevant excited electronic states. These CIS excitation energies are added to the ground-state Morse oscillator energies to construct the excited electronic state surfaces.Calculation of the excited electronic states provides the barrier height to C-C1 bond fission along the lowest adiabatic 'A" excited electronic state. In addition, the calculations also provide energetic splittings between the two lowest singlet adiabatic excited electronic states at the avoided crossing in the C-C1 bond fission channel for acetyl chloride and both the trans and gauche conformers of chloroacetone. Because the 'no nz=oexcited electronic state, accessed by a 308 nm photon, has a longer equilibrium C-0 bond length than in the ground electronic state, we present CIS calcu- lations of the avoided crossing region on the excited elec- tronic surfaces at a variety of C-0 bond lengths which represent the range of C=O stretching motion likely sampled by the dissociative wavefunction.Identification of Primary Product Channels :Resultsand Analysis Primary C-Cl and C-C Bond Fission in Chloroacetone When chloroacetone is excited at 308 nm in the '[n(O), n*(C=O)] absorption band, either the C-Cl bond, or the C-C bond will break; the data shows competition between the two bond fission channels. Fig. 13 shows the photofrag- ment TOF spectra taken at m/z+ = 49,ClCHl ,with 700000 laser shots and a 200°C nozzle.All of the signal was attrib- uted to primary C-C fission: ClCH,COCH, + hv(308 nm) -,ClCH, + COCH, (6) Through forward convolution fitting of the ClCH; spectrum, a centre-of-mass (c.m.) translational energy distribution, P(E,) (Fig. 14) was derived for C-C bond fission which peaks near very low energies, but extends out near 5 kcal mol-' or approximately one-third of the 13 kcal mol-' 30 available energy. Fig. 15 shows the photofragment TOF spectrum taken at m/z+ = 35, Cl', with 200000 laser shots and a 200°C nozzle. All of the signal except for a shoulder on the slow edge was attributed to primary C-Cl bond fission: ClCH,COCH, + hv(308 nm) -+ C1+ CH,COCH, (7) A forward convolution fit of the portion of the C1+ spectrum attributed to primary C-Cl bond fission gave a translational energy distribution (Fig.16) peaking near 5 kcal mol-' indi-cating that a significant portion of the available energy goes t For both molecules we use the typical C-0 (169 kcal mol-') and C-C (80 kcal mol-') bond energies reported in ref. 3qa). For the C-Cl bond energy in both chloroacetone and acetyl chloride, we use the 83.5 kcal mol- ' bond energy for acetyl chloride reported in ref. 3qb). J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 lmO E 1 3 0.8 1 100 200 300 400 500 600 700 timeofarrival/ps Fig. 13 Laboratory time-of-flight spectrum of the photofragments detected at 35C1CH: from chloroacetone photodissociated at 308 nm with an unpolarized laser. The source angle was 15".All of the signal results from primary C-C bond fission and is fit with a P(E,) shown in Fig. 14. 140 .... r-...i....i....i....~..... 0 120 ; a 100 -0 h+ 80 0luu 0601 40 a 020 -a....l....l....i....I...rlr.=...'-.~.. 0.8 g 0.6 W hcW 0.4 P 0.2 0 100 200 300 400 500 600 700 time ofarrival/ps Fig. 15 Laboratory time-of-flight spectrum of the photofragments detected at 35Cl+ from chloroacetone photodissociated at 308 nm with an unpolarized laser. The source angle was 15". The contribu- tion from ClCH, fragments to the C1' spectrum was determined by fitting the signal with the P(E,) in Fig. 14 derived from forward con- volution fitting the ClCHi signal. The rest of the signal results from the C1 fragments produced in primary C-Cl bond fission and is fit with the P(E,) in Fig.16. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 100 80 60 40 20 0 Fig. 16 Centre-of-mass product translational energy distribution, P(E,), for the C-Cl bond fission channel in chloroacetone at 308 nm. The P(E,) is derived from forward convolution fitting the portion of the C1+ signal which results from primary C-Cl bond fission in Fig. 15. to translation. The distribution for primary C-C fission fits the slow shoulder in the C1+ spectrum. In addition, the TOF spectrum shown in Fig. 17, taken at m/zf = 42, COCH;, with a 200°C nozzle and 4OOOOO laser shots, and the weaker signal at m/z+ = 43, COCH;, (Fig. 18) after 500000 laser shots, show significant contributions from both the C-Cl and the C-C bond fission channels.The fast component of the COCH; spectra, peaking near 320 ps, which was fitted with the translational energy distribution for primary C-Cl fission shown in Fig. 16, results from primary CH,COCH, fragments cracking in the ionizer to give COCH; daughter ions. Similarly, the slow component of the COCH; spectrum peaking near 360 ps and fitted with the translational energy distribution for primary C-C bond fission shown in Fig. 14, results from primary COCH, fragments cracking in the ionizer to COCH; daughter ions. Thus all the signal observed in the TOF spectra could be fitted by just two primary bond fission channels using the kinetic energy dis- tributions in Fig.14 and 16. The kinetic energy distributions of the C-Cl and the C-C bond fission products both evidence significant prob- ability for dissociation events imparting several kcal to rela- tive product translation. This indicates that, for both 1.0 1 100 200 300 400 500 600 700 time of arrival/ps Fig. 17 Laboratory time-of-flight spectrum of the photofragments detected at CH,CO from chloroacetone photodissociated at 308+ nm. The nozzle temperature was 200°C and the source angle was 15". The contribution from CH,COCH, fragments to the CH,CO+ signal was determined by fitting the signal with the P(E,) for primary C-CI bond fission in Fig. 16. Similarly, the contribution from COCH, fragments to the spectrum was determined by fitting the signal with the P(E,) for primary C-C bond fission shown in Fig.14. 1593 1.5 1.o h v)c.-5 $ 0.5 a W h c W zo 100 200 300 400 500 600 700 time of arrival/ps Fig. 18 Laboratory time-of-flight spectrum of the photofragments detected at CH3CO+ from chloroacetone photodissociated at 308 nm. The source angle was 15". Although the signal is rather noisy, the data are approximately fitted assuming contributions from both C-C and C-Cl bond fission, using the P(E,)s in Fig. 14 and 16. channels, dissociation proceeds via a reaction coordinate that has a significant exit barrier (barrier to reverse reaction) so the fragments exert a repulsive force on each other as they separate. Thus the pathway to dissociation probably does not involve internal conversion to the ground electronic state, as the barrier to reverse reaction on the ground state is negligi- ble.The pathway for C-Cl fission in chloroacetone is likely the same.as that for C-Cl fission in acetyl chloride upon excitation in the [n(O), n*(C-O)] absorption, which occurs on an A potential-energy surface resulting from the avoided electronic crossing of the no n;=o, and the n,, o&-, configu-rations and has a substantial exit barrier.26 Angular Distribution of the C-C1 Fission Product In bromacetone,'* the first hint of the influence of molecular conformation on the competition between C-C and C-Br fission came out in the comparison of the measured and pre- dicted photofragment angular distributions.For chloroace- tone, the data is more ambiguous. Below we analyse the angular distributions of the C1 fragments from C-C1 fission in chloroacetone at 308 nm. Fig. 19 shows the integrated C1 fragment signal from C-Cl bond fission us. OLAB,the angle between the laser elec- tric vector and the detector axis. The best fit to the photo- fragment angular distribution is obtained by varying the anisotropy parameter, B, in the classical electric dipole expressionJ2 Because Oc.m. is the angle between the recoil direction of the photofragment in the centre-of-mass frame and the electric vector of the light in the laboratory frame, fitting the data involves converting between the centre-of-mass and labor- atory frames using the measured molecular beam velocity and the P(E,) derived from the unpolarized data.The foward convolution fit of the data showed the photofragment aniso- tropy for C-Cl bond fission to be nearly isotropic, though slightly parallel with /3 = 0.1. This almost isotropic distribu- tion has two possible causes. One is that the angular distributions resulting from the dissociation of each con-former combine in such a way as to cancel out any individual anisotropy. Since the angle between the transition moment and the C-Cl bond is different in each conformer we might expect the angular distribution to reflect a weighted average of the two individual angular distributions. We can predict what the anisotropy parameter for each conformer would be if the transition moment were the same as that for the '[n(O), 1594 C 5: 850 000 800 In N f Q 750 cn w 3 70000 W 650 600; '' '' a ' '' '' ' ' 40 80 120 160 200 laboratory polarization angle/degrees Fig.19 Laboratory angular distributions of the C1+ signal which results from primary C-C1 bond fission in chloroacetone photo- dissociated at 308 nm with linearly polarized light. @ is the angle of the laser electric vector with respect to the detector axis (measured in the opposite sense of rotation as the source angle). The data points represent the integrated experimental TOF signal measured at four different laser polarization angles. The data points represent signal integrated between 180 and 273 ps corresponding to laboratory velo- cities of 18.1 x lo4 to 27.6 x lo4 cm s-'.Line fits show the predicted change in detected scattered signal intensity with laser polarization angle obtained, after transformation from the centre-of-mass to laboratory frame, with three trial anisotropy parameters, /I= 0.0,fi = 0.1 and fi = 0.2. n*(C=O)] transition in formaldehyde and bromoacetyl chlo- ride in the limit that photofragment recoil is axial, along the C-C bond direction, and prompt with respect to molecular rotation. We take the '[n(O), n*(C50)J transition moment to be in the C-C=O plane and perpendicular to the C=O bond axis. In the trans conformer, the 35.0" angle (using the calculated equilibrium geometry given in Table 3) between the C-Cl bond and the direction of the electronic transition moment gives a predicted fit,,, = 2P2(c0s 35.0") = 1.01, while in the gauche conformer the predicted anisotropy is flgouehhe = 2P2(cos 77.0") = -0.99.Assuming a thermal population of trans and gauche with the gauche the more stable by 0.86 kcal mol-' 33f and assuming no conformational cooling in the expansion,2' the experimental nozzle temperature of 200 "C gives 83% gauche and 17% trans in the molecular beam. Weighting the predicted fi values for the gauche and trans conformers by their relative populations gives a predicted /? = 17% (1.01) + 83% (-0.99) = -0.65 for comparison with the experimental data. If the C-Cl : C-C fission branching ratio were the same for both conformers, this calculated average anisotropy parameter should predict the angular distribution of the C1 atom fragments well.Thus, as long as the dissociation is prompt, since the data shows a distribution which is slightly parallel as opposed to the predicted perpendicular distribu- tion, there must be a smaller contribution to the Cl atom signal from the gauche conformer than the prediction leads us to expect. Indeed to get an average of fi= 0.1, the minor trans conformer must have a larger C-Cl :C-C fission branching ratio than the gauche conformer by a factor of almost five. Therefore, as for C-Br fission in bromoacetone, C-Cl fission dominates in the trans conformer. Unlike in bromoacetone, however, where C-Br fission occurs almost exclusively from the anti conformer, in chloroacetone C-Cl fission may also be a minor channel in the gauche conformer.~-~~ t This translgauche energy difference was determined using infra- red spectra and ab initio calculations. The ab initio values varied widely with basis set, and we use this value with reservations. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 It is also possible that a small amount of C-C fission is seen from the trans conformer. This nearly isotropic angular distribution may also result from a dissociation which is slow with respect to molecular rotation, because the dissociation proceeds through a mecha-nism such as intersystem crossing. In bromoacetone, the strongly anisotropic parallel angular distribution was shown to result from C-Br fission occurring almost exclusively from the anti conformer.If the C-CI fission in chloroacetone is also largely from the trans conformer, but slow with respect to molecular rotation, we might expect just this parallel, but nearly isotropic angular distribution. It is difficult to say just why C-Cl fission should be slower in chloroacetone than in bromoacetone or acetyl chloride. One possibility is that in acetyl chloride, photoexcitation accesses the excited singlet state at energies above the barrier to C-Cl fission on the singlet surface, while in chloroacetone, it does not, so disso-ciation must proceed via intersystem crossing to the triplet surface. Otherwise, the mechanism is largely the same, as the barrier to C-Cl fission on the triplet surface is also from an avoided crossing between the no n&o and n,, CJ&, configu-rations.If the timescale for intersystem crossing is on the order of tens of picoseconds or more, this mechanism could result in the nearly isotropic angular distribution we mea- sured for chloroacetone. Intersystem crossing might also account for the slightly smeared angular distribution mea-sured in bromoacetone. (Bromine's larger mass would con- tribute to increased spin-orbit coupling to speed the intersystem crossing rate.) In addition, since the rotational period for chloroacetone is faster than that for bromo-acetone, more smearing of the angular distribution would be expected in chloroacetone for a process of similar timescale.Changing the Populations of the Molecular Conformers to Sample Different Regions of the Conical Intersection If, as in bromoacetone, C-C fission proceeds predominantly from photoexcitation of the gauche conformer, where it can dissociate adiabatically through the conical intersection, and C-C1 fission dominates in the trans conformer, because the competing C-C fission channel is non-adiabatically sup- pressed at near-planar geometries, then we should be able to alter the observed branching ratios by changing the relative populations of gauche and trans conformers in the molecular beam. Assuming little conformational cooling in the expan- sioq2' we can increase the fraction of the higher (by ca. 0.86 kcal mol- energy trans conformer in the molecular beam by increasing the nozzle temperature.Fig. 20 compares the m/z+ = 35, C1+, time-of-arrival spectrum taken at a 100°C nozzle temperature, where there are significant contributions from both primary C-Cl and primary C-C bond fission, with the same spectrum taken at a 400°C nozzle temperature. The spectra in Fig. 20 show that the increased population of the trans conformer at 400°C results in a decreased contribu- tion to the Cl+ signal from primary C-C fission relative to the signal from C-Cl bond fission. To identify separately the two contributions to the C1+ daughter ions' spectrum, we cal- culate the predicted arrival time spectrum of the ClCH, product of C-C fission and the C1 product of C-Cl fission using the individually measured kinetic energy distributions for C-C and C-Cl fission shown in Fig.14 and 16. We then change the relative probability of each bond fission channel until a good fit to the spectra in Fig. 20, with contri- butions from both, is achieved. The percentage contribution from each bond fission channel that fit the C1+ data are at 100°C: 96.5% from primary C-Cl bond fission and 3.5% from primary C-C bond fission, us. that at 400°C nozzle temperature: 97.5% from primary C-Cl bond fission and J. CHEM. SOC.FARADAY TRANS., 1994, VOL. 90 1.2 .... I....(....(....,....(.... 1.0 -: (a) 0b 5 0.8 -.-C 0.6 -4 Y 0.4 -cW 0.2 1 0-1.2 1.o h .-v) 0.8 CI C 0.6 W 0.4 hcW z0.2 0 c 4 ..............................i 100 200 300 400 500 600 700 time ofarrival/ps Fig. 20 Laboratory time-of-flight spectra at two nozzle tem-peratures of the photofragments detected at 35Cl+from chloroace-tone photodissociated at 308 nm: (a) with a nozzle temperature of 100“C;(b)with a nozzle temperature of 400 “C.The source angle was lo” for both spectra. 2.5% from C-C bond fission. These percentages already include corrections for kinematic factors and angular dis-tribution, but must be weighted by the relative ionization cross-section for Cl and ClCH, fragments and the probability of giving C1+ daughter ion to obtain absolute C-Cl : C-C branching ratios. Although we cannot obtain an absolute C-Cl : C-C fission branching ratio at each conformational temperature because the daughter-ion cracking pattern of ClCH, is unknown, we can obtain a precise measure of the relative branching ratio change and compare it directly to the relative change in conformer populations.Assuming no cooling of conformer populations in the expansion,” the relative change in conformer population in heating the nozzle from 100 to 400°C is: 400”~:f anti \ fC-Cl\ t 100°C: (0.264) (0.158) predicted = 1.7 (9) giving a predicted increase in the C-Cl : C-C branching ratio of 1.7 assuming C-C fission dominates in the gauche conformer and C-Cl fission dominates in the trans con-former. The experimentally observed change in branching ratio is slightly lower : c-Cl 97.5% (C-CJ400 -(2.5% ) - 1.4400=observed c-c1 --= la4 (10) /c-Cl\ 96.5%(c-c)loo(3.5%) It is clear that increasing the fraction of trans conformer in the beam and decreasing the fraction of gauche conformer results in a corresponding increase in the branching to C-Cl fission and decrease in the branching to C-C fission.This result is in accord with the model presented for bromo-acetone, in which dissociation from the trans conformer accesses regions of the C-C fission reaction coordinate near the conical intersection, where it is non-adiabatically inhib-ited and competes less effectively with C-Cl fission, and dis-sociation from the gauche conformer proceeds through regions of the conical intersection where the surfaces are further split from each other, so the C-C dissociation can proceed adiabatically and dominate C-C1 fission.Results of Ab Znitio Calculations The experiments indicate that there is competing C-C and C-Cl bond fission in chloroacetone, but earlier experiments on acetyl chloride showed no evidence of C-C fission.26To determine whether non-adiabatic recrossing of the reaction barrier to C-C1 fission could be in part responsible for these observations, we investigate the energy splitting between the ‘A” excited potential-energy surfaces at the avoided crossing. Since the interaction of electronic configurations is in part controlled by the distance between the orbitals involved in the configuration crossing, we expect a larger splitting in acetyl chloride, where the distance between the C-Cl and CEO chromophores is smaller by one CH, group than that in chloroacetone.The ab initio calculations, described in detail below, do show a larger splitting, so, on average, C-Cl fission should proceed more adiabatically in acetyl chloride than in trans-chloroacetone (see Fig. 21, left and centre frames). We also investigate the conformational dependence of the C-C : C-Cl branching. Fig. 21 shows cuts along the C-C1 stretch of the calcu-lated singlet excited electronic states of acetyl chloride (left), trans-chloroacetone (centre) and gauche-chloroacetone (right). Although at this level of ab initio calculation the surfaces are approximate and barrier energies are known to be too high, the calculations still provide useful qualitative information.The electronic character of the lowest ‘A” potential-energy surface in trans-chloroacetone, as determined by the domi-nant electronic configuration in the GAUSSIAN 92 output, plainly changes from no ~n,*=~,(a”’’), in character to n,, o&,, (a“a’), in character across the barrier to C-Cl fission, as expected for an adiabat resulting from the avoided electronic curve crossing of these two electronic configurations. Simi-larly, the electronic configuration of the first excited singlet state of acetyl chloride evolves from mixed character, no @=o, (a’a”) and n,, X& o, (a”’’), in the Franck-Condon region, to ncla&-l, (a”a’),after the barrier. The lowest repul-sive A’ surface for both molecules, characterized by an in-plane na electronic configuration, does not interact with the A“ states so is not shown in the figure.However, since there are no symmetry restrictions in the gauche conformer of chloroacetone, in principle all three of the electronic states can mix and avoid each other. The right-hand frame of Fig. 21 clearly shows this is not the case, that one of the three states does not interact strongly with the other two, while the other two show an avoided curve crossing which forms the adiabatic reaction coordinate for C-Cl fission. For this reason we consider only the two interacting electronic states in the analysis of the avoided crossing which forms the barrier to C-Cl fission. Table 5 summarizes the results of the calculations by showing the energy of the lowest-excited electronic state and the splitting between the adiabats obtained from several one-dimensional cuts at various C-0 bond lengths.The splitting J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 acetyl chloride trans -chloroacetone gauche -chloroacetone 482001-1 80000 50000 80000 47400 80000 7000070000 4 49600 70000 46600 2.43 2.46 2.49 2.51 2.542.23 2.24 2.25 2.27 2.28 2.37 2.38 2.39 2.41 2.42 60000 60000 \ c ---\JP'-'* I E 50000Y> 00;40000 -0 *#I Q, 30000 -50000 -\ 0% 40000 % -% 0 -% 300001 4 30000120000y,;ooool/, 10000 0 1.8 2.1 2.4 2.7 3.0 1.8 2.1 2.4 2.7 3.0 R,c,lA R,c,lA Fig. 21 Cuts through the calculated ab initio electronic surfaces, at equilibrium C-0 bond lengths, for acetyl chloride with R(C-0) = 1.19 A (left), trans-chloroacetone with R(C-0) = 1.2454 8, (centre), and gauche-chloroacetone with R(C-0) = 1.2508 A (right).Although for the gauche conformer all three electronic states can in principle mix and split, it is clear that one of the three states does not interact strongly with the other two. The avoided crossing of the two other states forms the adiabatic reaction coordinate for C-C1 fission, just as the avoided crossing of the two 'A states does in trans-chloroacetone and acetyl chloride. The boxed-in portions at the barrier to each bond fission pathway, which are enlarged in the insets above each plot, show that the splitting between adiabats at the barrier to C-Cl bond fission in trans-chloroacetone is, on average, much smaller than that in acetyl chloride.Although the increase in splitting in going from trans-to gauche-chloroacetone has a negligible effect on the observed branching, it is consistent with a now Woodward-Hoffmann-allowed C-C1 bond fission in the gauche conformer. For the particular cuts along the avoided crossing seam shown here, the splitting at the avoided crossing to C-Cl fission is 407 cm-' in acetyl chloride, 1499 m-' in gauche-chloroacetone and only 88 cm-'in trans-chloroacetone. Other cuts are given in Table 5. varies along the seam of the avoided crossing; the avoided crossing occurs at longer C-C1 bond distances, with split- tings usually decreasing, for cuts taken at longer C-0 dis-tances. Although the splitting varies along the avoided crossing seam it is, on average, larger in acetyl chloride than in trans-chloroacetone (see left and centre frames of Fig.21). Note that in preliminary calculations using more extensive basis sets, we found the magnitude of the splitting to be basis set dependent, but acetyl chloride still had a larger splitting than trans-chloroacetone. The increased proximity of the interacting orbitals in acetyl chloride increases the splitting and trajectories are more likely to traverse the barrier to C-Cl fission adiabatically. This could allow the C-Cl fission to dominate C-C fission in acetyl chloride. Another possible reason for the appearance of C-C fission in chloroacetone is the facility of C-C fission from the gauche conformer in particular.Populating the gauche con- former, in effect, moves the dynamics to a region of phase space far from the conical intersection formed by the Franck- Condon excited no &,,and repulsive aok configurations, so the splitting between adiabats at the avoided crossing is larger. Although zero-point vibrational motion also breaks C,symmetry in acetyl chloride and trans-chloroacetone, the splitting between adiabats near the conical intersection is still necessarily small and C-C fission is suppressed. Only large distortions from planar geometry allow dissociative trajec- tories to access regions of the conical intersection where split- ting between adiabats is large.If one could access very non-planar geometries for acetyl chloride, one might see a contribution from C-C fission. This conical intersection is largely responsible for the con- formational dependence of the ratio of C-C to C-Cl bond fission in chloroacetone. From examination of Table 5 it is clear that the splitting at the barrier to C-Cl fission is con- sistently larger (by at least a factor of seven, and as much as a factor of 30) in gauche chloroacetone than in the trans con- former for equivalent C-0 distances. The smaller energetic splitting between the two 'A adiabats in the trans conformer results in a larger probability of non-adiabatic recrossing of the C-C1 fission transition state, thereby reducing the rate constant for C-Cl bond fission.Experimentally it is observed, however, that the ratio of C-C1 to C-C bond fission in trans-chloroacetone must be larger than that in the gauche conformer. Even though C-C1 fission can occur more adiabatically in the gauche conformer than in the trans, in gauche-chloroacetone the adiabats along the C-C stretch coordinate strongly avoid each other, so C-C fission occurs easily. Thus, C-Cl and C-C bond fission effectively compete. The presence of large non-adiabatic effects along the C-C fission reaction coordinate in trans-chloroacetone suppresses C-C fission, allowing C-Cl fission to dominate. 6. Summary The experiments and models described within show that in the class of reactions known as Woodward-Hoffmann for- bidden, the failure of the Born-Oppenheimer approximation can result in a marked reduction in reaction rate, changing the expected branching between energetically allowed chemi- cal bond fission channels.Experiments on bromoacetyl and brompropionyl chloride reviewed here elucidate the intramol- ecular distance dependence of the non-adiabatic recrossing of the barrier to C-Br fission. Work on bromoacetone further investigates the conformation dependence of non-adiabatic recrossing in both Woodward-Hoffmann-forbidden reactions J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 5 Summary of ab initio calculations of the splitting between adiabats at the barrier to C-C1 bond fission in acetyl chloride, trans- chloroacetone and gauche-chloroacetone trans-Chloroacetone Barrier to C-C1 bond fission energy/cm-' at barrier on 'A", referenced to Ro,, at barrier/A minimum in the ground state 2Vl2/cm-1 ~~ 1.oo 2.06 99 227 168 1.19 2.32 51 715 108 1.25 2.40 47 457 88 1.34 2.53 45 414 69 1.54 2.72 52 005 48 gauche-Chloroacetone Barrier to C-C1 bond fission energy/cm-' at barrier on first excited singlet, at barrier/A referenced to minimum in the ground state 2V' -1 1.oo 2.17 85 117 4996 1.19 2.42 33 664 2033 1.25 2.51 27 291 1499 1.34 2.65 22 626 958 1.54 2.95 23 405 372 Acetyl Chloride Barrier to C-Cl bond fission energy/cn-' at barrier on 'A, referenced to R(c-l, at barrier/A minimum in the ground state 1.00 2.04 33 069 1225 1.19 2.25 12 861 407 1.25 2.32 12991 240 1.35 2.43 16 524 50 1.55 2.56 27 978 1327 The first two columns give the CEO and C-C1 bond lengths, in A,at the barrier.The third column shows the calculated energy at the barrier of the lowest (of A" symmetry for acetyl chloride and trans-chloroacetone) singlet excited adiabatic electronic surface (referenced to the minimum energy in the ground state). The fourth column, labeled 2VI2, shows the splitting between the two adiabats at the barrier formed from the avoided electronic curve crossing. Only the C-C1 bond length was varied to find the avoided crossing; the C-0 bond lengths are listed in column 1, all other internuclear geometries are frozen at the equilibrium geometry given in Tables 3 and 4.and reactions proceeding through a conical intersection. In 3 P. J. Robinson and K. A. Holbrook, Unimolecular Reactions, both the previous work on bromoacetone and the new work on chloroacetone, the data indicate that the conformation dependence of non-adiabatic recrossing near the conical intersection plays a major role in determining the difference in branching between C-X (X-C1, Br) and C-C fission in the two molecular conformers. 4 5 6 Wiley Interscience, London, 1972. R. D. Levine and R. B. Bernstein, Molecular Reaction Dynamics and Chemical Reactivity, Oxford University Press, New York, 1987, section 5.6, pp. 296-299. M. Born and R. Oppenheimer, Ann. Phys., 1927,84,457. (a) M. G. Evans and M.Polanyi, Trans. Faraday SOC., 1935, 31, 875; (b) M. G. Evans and M. Polanyi, Trans. Faraday SOC., 1938, 34,ll; (c) E. Wigner, Trans. Faraday SOC.,1938,34,29. This work was supported by the National Science Founda- tion, currently under renewal grant number CHE-9307500. We gratefully acknowledge Prof. M.M. Francl's contribution to the early work reviewed here; the collaboration was sup- 7 8 9 G. L. Closs and J. R. Miller, Science, 1988,240,440 J. C. Tully, in Dynamics of Molecular Collisions Pt. B, ed. W. H. Miller, Plenum Press, New York, 1976, p. 217. L. Salem, Electrons in Chemical Reactions, Wiley-Interscience, New York, 1982. See also L. Salem, J. Am. Chem. SOC., 1974,%, ported by a Summer Faculty Research Fellowship, a supple- ment to our grant (no.22218-AC6) from the donors of The Petroleum Research Fund, administered by the ACS, and by the Rosalyn R. Schwartz Lectureship. L.J.B. acknowledges the support of a Camille and Henry Dreyfus Foundation Teacher-Scholar Award and an Alfred P. Sloan Research 10 11 3486. (a) M. D. Person, P. W. Kash, S.A. Schofield and L. J. Butler, J. Chem. Phys., 1991, 95, 3843; (b) M. D. Person, P. W. Kash and L. J. Butler, J. Chem. Ph.ys., 1992, 97, 355; (c) P. W. Kash, G. C. G. Waschewsky and L. J. Butler, J. Chem. Phys., 1994,100,4017. P. W. Kash, G. C. G. Waschewsky, L. J. Butler and M. M. Francl, J. Chem. Phys., 1993,W, 4479. Fellowship. Two undergraduate co-workers, John Page and Michele Auer, made a significant contribution to the compu- tational work on the acetyl chloride and chloroacetone sys tems.12 13 P. W. Kash, G. C. G. Waschewsky, R. E. Morss, L. J. Butler and M. M. Francl, J. Chem. Phys., 1994,100,3463. R. B. Woodward and R. Hoffmann, The Conservation of Orbital Symmetry, Verlag-Chemie, Weinheim, 1970; S. S. Shaik, J. Am. Chem. SOC., 1981,103,3692. References 1 K. J. Laidler and M. C. King, J. Phys. Chem., 1983,87, 2657. 2 D. L. Truhlar, W. L. Hase and J. T. Hynes, J. Phys. Chem., 1983, 14 15 16 17 D. M. Silver, J. Am. Chem. SOC., 1974,%, 5959. (a) J. Michl and V. Bona&iC,-Koutecky, Electronic Aspects of Organic Photochemistry, Wiley, New York, 1990, p. 20. (b) p. 276. A. G. Evans and M. G. Evans, Trans. Faraday SOC., 31, 1400 (1935). See W. F. K. Wynne-Jones and H. Eyring, J. Chem.Phys., 1935, 87,2664. 3,492. 1598 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 18 19 J. K.Burdett, personal communication. See D. M. Cyr, G. A. Bishea, M.G. Scarton and M. A. Johnson, J. Chem. Phys., 1992, 97,5911; S. S. Shaik, J. Am. Chem. SOC., 28 29 M. D. Person, Ph.D. Thesis, Department of Chemistry, Uni- versity of Chicago, 1991. GAUSSIAN 92, Revision C, M. J. Frisch, G. W. Trucks, M. 20 21 1982,104,2708. See, eq. S. L. Mielke, G. J. Tawa, D. G. Truhlar and D. W. Schwenke, J. Am. Chem. SOC.,in the press. R. S. Ruoff, T. D. Klots, T. Emilsson and H. S. Gutowsky, J. Head-Gordon, P. M. W. Gill, M. W. Wong, J. B. Foresman, B. G. Johnson, H. B. Schlegel, M. A. Robb, E. S. Replogle, R. Gomperts, J. L. Andres, K. Raghavachari, J. S. Binkley, C. Gon- zalez, R. L. Martin, D. J. Fox, D. J. Defrees, J. Baker, J. J. P. 22 23 Chem. Phys., 1990,93,3142. (a) G. E. Busch and K. R. Wilson, J. Chem. Phys., 1972, 56, 3638; (b) S. C. Yang and R. Bersohn, J. Chem. Phys., 1974, 61, 4400; (c) J. R. Durig, J. Lin and H. V. Phan, J. Ramun Spectrosc., 1992,23, 253. T. H. Lowry and K. S. Richardson, Mechanism and Theory in 30 31 Stewart and J. A. Pople, Gaussian, Inc., Pittsburgh PA, 1992. (a) A. J. Gordon and R. A. Ford, The Chemist’s Companion, Wiley, New York, 1972; (b) J. A. Devore and H. E. ONeal, J. Phys. Chem., 1969,73,2644. K. Yates, S. L. Klemenko and I. G. Csizmadia, Spectrochim. Acta, Part A, 1969,25, 765. Organic Chemistry, Harper and Row, New York, 1987, p. 1041. 32 R. N. Zare, Mol. Photochem., 1972,4,1. 24 25 26 See M. Reinsch and M. Klessinger, J. Phys. Org. Chem., 1990,3, 81, and references therein. N. C.Yang and E. D. Feit, J. Am. Chem. SOC.,1968,90,504. See M. D. Person, P. W. Kash and L. J. Butler, J. Phys. Chem., 33 J. R. Durig, J. Lin, C. L. Tolley and T. S. Little, Spectrochim. Acta, Part A, 1991,47, 105. 27 1992,%, 2021 and references therein. Y. T. Lee, J. D. McDonald, P. R. LeBreton and D. R. Hersch- Paper 3/05223K; Received 27th August, 1993 bach, Rev. Sci. Instrum., 1969,40, 1402.

ISSN:0956-5000    

DOI:10.1039/FT9949001581

出版商:RSC    

年代:1994

数据来源: RSC

摘要:

J. CHEM. SOC. FARADAY TRANS., 1994, 90(12), 1599-1604 Concerted and Stepwise Mechanisms in Cycloaddition Reactions : Potential Surfaces and Isotope Effects Kendall N. Houk,* Yi Li, Joey Storer, Laura Raimondi and Brett Beno Department of Chemistry and Biochemistry, University of California, Los Angeles, Los Angeles, CA 90024-1569,USA ~ CASSCF/6-31G* calculations have been performed on concerted and stepwise Diels-Alder reactions of buta- diene with ethene, the dimerization of butadiene, and the dimerization of cyclobutadiene. The relative energies of concerted and stepwise mechanisms are compared, and the factors influencing these 'energies of concert' are discussed. The comparison of calculated isotope effects to experimental data provides support for theoreti- cal results.Until recently, many theoretical studies of the Diels-Alder reaction have focused on the parent system of butadiene and ethene. All ab initio and most semi-empirical computational methods now agree closely as to the geometry of the con- certed transition state,' while MCSCF and CI calculations give qualitatively similar geometries for the stepwise path. The furious debate2 between semi-empiricists and ab initioists has ~ubsided.~ Experiment places the stepwise mechanism 2-7 kcal mol-' above the concerted mechani~m.~ As dis-cussed later, theory gives a small energy difference for the concerted and stepwise mechanisms, the magnitude of which is not known precisely. The difference between activation energies for the con-certed and stepwise reactions is defined by Doering as the 'energy of concert'.' The energy of concert of the butadiene- ethene reaction has been estimated as 7 kcal mol-'.For the butadiene dimerization the energy of concert is only 1-2 kcal mol-',suggesting a significant substituent effect. The reac- tion of benzene with ethene has a large energy of concert.' Apparently, much of the benzene aromaticity is preserved in the transition state of the concerted process, while in the dira- dical intermediate the aromaticity is disrupted. At the other extreme, the reactions of cyclobutadiene as a diene or die- nophile may not have a significant energy of concert, since an anti-aromatic species is essentially already a biradical which can readily undergo attack on an alkene (essentially a radical addition) to form a biradical intermediate.In this paper, the latest MCSCF calculations on the con- certed and stepwise Diels-Alder reactions of butadiene and ethene are reported and compared to these two reaction paths for the dimerizations of butadiene and cyclobutadiene. Full details of these computational results will be published ~eparately.~?~ CASSCF calculations were performed with GAMESS7 uti- lizing both 3-21G and 6-31G* basis sets. The Pulay criterion was used to define the active space for each system.8 The relative energies of various species were calculated with the QCISD(T) method on MCSCF geometries. ButadieneEthene Reaction The geometries of stationary points obtained with six-electron/six-orbital CASSCF/3-21G and CASSCF/6-31G* calcuations are summarized in Fig.1, and the relative ener- gies assessed by various computational methods are given diagrammatically in Fig. 2. The concerted transition structure 2 of the butadiene-ethene reaction is very much like those reported at various levels of theory. Unlike the work of Ber- nardi et al. with CAS/4-3 1G calculation^,^ we could locate both a transition structure 3 and a biradical intermediate 4 for the stepwise pathway. We were unable to find either an asynchronous transition structure or a biradical minimum when the methylene radical centre in 3 or 4 is rotated syn-gauche to the ally1 moiety. This result indicates that there is a very small potential-energy barrier, if any, for the closure of the biradical intermediate when the radical centres are in a conformation where interaction is possible.There is no asyn- chronous concerted transition state. The only stepwise mechanism of the parent Diels-Alder reaction involves for- mation of 4 in the rate-determining step, followed by rotation about C(4)-C(5) involving a second barrier of 2-3 kcal mol-' accompanied by collapse with no further barrier to cyclohexene. A small barrier of 2 kcal mol-' is found for the cleavage of biradical intermediate 4 via a-bond breakage involving tran- sition structure 3, while in the simpler butane-l,ediyl system," there is no potential-energy barrier for the disso- ciation of the butanediyl biradical into two ethenes."' The 2 kcal mol- 'stabilization of biradical4 results from allylic res- onance. As shown in Fig.2, single-point energy calculations at the RQCISD(T)/6-3 lG* level using the CASSCF/6-3lG* geome- tries predict that the concerted transition structure 2 is 10 kcal mol-' more stable than the stepwise transition structure 3, and 4 kcal mol-' more stable than the biradical interme- diate 4. This RQCISD(T) method, using a single determinant -1.397 (2.223) (1.404) 1 2 " 1.490 3 4 Fig. 1 CASSCF/3-21G (CASSCF/6-31G*) reactants (l),transition structures (2 and 3), and biradical intermediate (4) of the Diels-Alder reaction of butadiene with ethene. Bond lengths are in A. -45.7-43.8 . . -..A . ..40.7 -35.7 -25.5 -11 37.3 40.7 25.5 25.132 CASSCF CASSCF UQCISD(T) RQCISD(T) exptl. 3-21G 6-31G* 6-31GR 6-31G* Relative energies (kcal mol- ') of reactants, transition struc- tures, and biradical intermediates at different computational levels for the Diels-Alder reaction of butadiene and ethene wavefunction, offers a substantial improvement of the calcu- lated relative energies over RHF or even MP2/MP4 methods. In fact, the calculated activation energy of 25.5 kcal mol-' is very close to the experimental value, much better than results from other calculations. Is there any support for the concerted mechanism and the geometry of the transition state obtained? In order to cali- brate theory with experiment, we have calculated isotope effects for the concerted and stepwise mechanisms of the Diels-Alder reaction of butadiene and ethene."" Several results are given in Fig.3. The calculations are for the butadiene-ethene reaction. The only experiments available are from Gajewski's experiments on nearly symmetrical reac- tants.' Ib The calculated isotope effects for the concerted reac- tion are considerably larger than for the stepwise reaction. In fact, the experimental data for the symmetrically disub- Theorv (MCSCFt6-13Gf) CX2 II -((3+ y2 y2 0.95 0.97 0.90 0.94 Exmi-(373 K) + t -g"rzZ y2 z Z= t-CN 0.95 t-CO2Me 0.93 Z= t-CN 0.95 t-co2w 0.92 c-C02Me 0.92 Z= t-CN 0.90 t-CO2Me 0.85 c-C02Me 0.87 Fig. 3 Theoretical and experimental isotope effects for Diels-Alder Reactions' la** J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 1.23 1.28 Fig. 4 Theoretical and experimental isotope effects for some retro- Diels-Alder reactions 'la*' stituted cases are very close to expectation for a concerted process and quite different from those expected for the step- wise mechanism. Although there is no direct comparison of experimental and theoretical results, the comparison suggests that the reaction is concerted and synchronous. A more direct comparison is possible for the retro Diels- Alder reaction. Several examples are shown in Fig. 4. For the anthracene adduct reaction,"' a direct comparison between theory and experiment is available. Here there is clearly superior agreement between experimental data and predic- tions based on the concerted mechanism."" Butadiene Dimerization The butadiene dimerization could be studied only at the CASSCF/3-21G level because of the size of the system and the need to use eight-orbital/eight-electron calculations.Fig. 5 shows the transition structures and biradical intermediates located for the butadiene Diels-Alder dimerization. The rela- tive energies are summarized in Fig. 6. Though there are several possible conformations for the concerted transition structures, the exo transition structure with s-trans-butadiene as dienophile is favoured at the RHF/3-21G level. The s-cis exo and endo transition structures are each ca. 1 kcal mol-' above the s-trans exo structure. For the CASSCF studies, only the s-trans structures were studied.We located an endo transition structure for s-cis-butadiene and an exo transition structure for s-trans-butadiene reacting with the diene at the CASSCF level of theory. The exo transition structure 7 is only 0.2 kcal mol-' more stable than the endo transition structure 7'.This is a minor disagreement with the experi- mentally observed slight endo selectivity of the butadiene dimerization (endolexo ratio of 59 :41 at 1 bar).'* However, not all stereoisomers were studied. There is a slightly larger calculated and experimental endo preference for the Diels- Alder reactions of cyclopentadiene with various die-n0phi1es.l~ The concerted transition structure 7 is quite asynchronous; the two forming partial a-bonds are 2.07 and 2.39 A in length.The stepwise mechanism may involve the formation of the biradical intermediate 9 formed through the transition structure 8, followed by bond rotation and biradical ring closure. This stepwise mechanism is predicted to be favoured by 1 kcal mol-' over the concerted pathway with the CASSCF/3-21G calculations. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 .-a, 2.071 ', 2.389 '2.410 1.343 ' s-trans 6 7 7' s-cis 6' 8 9 .' 3.250 1. 10 11 12 Fig. 5 Geometries of some butadiene dimerization stationary points. CASSCFI3-21G reactants (6, 6), concerted transition struc- tures (7, 7'), transition structures (8, 10) for biradical formation, biradicals (9, 1l), and transition structure for biradical cyclization (12).Bond lengths are in A. Transition structure 10 has the same energy as 8. It leads to the biradical intermediate 11, which is isoenergetic with 9. Transition structure 10 has a forming a-bond length of 1.90 A, while there is no bonding between the other termini which are 3.25 A apart. The biradical 11 has a newly formed o-bond Fig. 6 CASSCF/3-21G relative energies (kcal mol-') of stationary points for butadiene dimerization 5 + 5-[-F]* -6 (38.9) 13 (-2.6) length of 1.61. There is a distance of 3.46 8, between the other termini which become bonded in cyclohexene. Biradical 11 undergoes ring closure uia transition structure 12 to form vinylcyclohexene. Transition structure 12 is extremely early, similar in structure to the biradical with a very long (2.81 A) forming single bond. The identical energies of 8 and 10 and of 9 and 11 indicate that there is no interaction between radical centres at dis-tances >3.25 A.The fact that 12 is a transition structure pro- vides an interesting (although not necessarily universal) value of 2.8 8, for the length of a forming bond in the transition state of biradical closure. The existence of both concerted and stepwise mechanisms with similar conformations in the butadiene dimerization is particularly interesting. Dewar14 has suggested that this is the case for the butadiene-ethene reaction, but it is not found. In the butadiene-ethene reaction, attempted opti- mization of an asynchronous structure similar to 11 leads to collapse to the synchronous transition structure.This differ- ence between the two systems is the result of allylic stabil- ization of the biradical intermediate in the butadiene dimerization which is not present in the butadiene-ethene reaction. At the CASSCF/3-21G level, the addition of a vinyl group destabilizes the concerted transition state 2 by 1 kcal mol-',stabilizes the transition state 3 leading to the diradical intermediate by 5.5 kcal mol-' and stabilizes the diradical intermediate 4 by 8.8 kcal mol-'. There are many potential biradical intermediates with various conformations. The transition structure 13, leading to biradical intermediate 14, is ca. 1 kcal mol-' more favour- able than 8 and 10 (Fig.7). This all-trans transition structure 13 is predicted to be 2.6 kcal mol-lower in energy than the concerted transition structure at the CASSCF/3-21G level. The trans, trans biradical 14 is more stable than the trans, cis biradical 11 by ca. 1 kcal mol-', and there is a similar 5 kcal mo1-' barrier for the cleavage of 14 into two butadienes. There is a substantial barrier to rotation in an ally1 radical, and consequently intermediate 14 can only readily form cis-or trans-divinylcyclobutane upon ring closure. A tran-sition structure 15 was located for the ring closure of a trans, trans biradical intermediate to form trans-divinylcyclobutane. As expected for the recombination of a biradical, this tran- sition structure is a very early one involving a long forming a-bond (2.52 A), and its energy is only 2-3 kcal mol- above the biradical minimum.Radical ring closure from the biradical is again kinetically favoured over reversion to buta- diene, although closure of the four-membered ring is predict- ed to be 1 kcal mol-' less favourable than closure of 11 to a six-membered ring. In the butadiene dimerization the energy of concert is pre- dicted by CASSCF/3-21G calculations to be negative by 1.3 kcal mol-'. In contrast, the energy of concert in the .... . . .* I>]# -'0 -._-._ -8'--. -. _...-14 (-7.4) 15 (-5.0) Fig. 7 CASSCF/3-21G transition structures and intermediates of butadiene [2 + 21 dimerization. Th!: energies relative to 7 are given in parentheses (kcal mol-').J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 4.59Ar 1.578 #(1.546) 1.577 1.360 (1.353) 1 16a 16b (triplet) 16c (two CBs) 16d (two CBs) 1.447 (1.433)1.400 (1.357) 'I1*I 08 , ,, b,1, i i 2.328 *I i (2.450) *I 8I,, I. (1.382)17 18 19 20 1.363 .' 2.303 1.513 21 22 23 (triplet, eclipsed) 24 (single, anti) Fig. 8 CASSCF/3-21G (CASSCF/6-31G*) optimized structures butadiene-ethene reaction is 5.8 kcal mol- ' at the same level. The difference is 7.1 kcal mol -'. The calculated energies of concert are in reasonable agree- ment with those found experimentally. Cyclobutadiene Dimerization The eight-electron/eight-orbital CASSCF/3-21G and CASSCF/6-3 lG* calculations for the cyclobutadiene dimer- ization are summarized in Fig. 8 and 9.6 Calculations on cyclobutadiene and several weak complexes are shown in structure 16a-d.Minimization of two rectangular CB mol- *lo]12.l 16b (triplet) 0 85.,,19 and 22 -m, 2m E2 68.5, 5320 16a 46.7-23 (triplet) 0 229.9 39.8 d 24 (singlet) 21 go.0 -7.2#-17 18 Fig. 9 CASSCF/3-21G energetics (kcal mol- ') for the stationary points on the cyclobutadiene dimerization potential-energy surface ecules held eclipsed in an orientation corresponding to a for- bidden [2 + 21 reaction led to a stationary point 16c with both 3-21G and 6-31G* basis sets. The face-to-face distance in the optimized supermolecule 16c is 4.6 A, and the two cyclobutadienes retain their localized rectangular structures.Structure 16c is 0.5 kcal mol-' higher in energy than two isolated cyclobutadienes, indicating that there is no attractive interaction between the two cyclobutadienes in 16c. Closed-shell repulsive interactions keep the two singlet cyclo- butadienes apart. Minimization with the rectangular cyclobutadienes held face-to-face in an orientation conducive to the [4 + 21 cyclo- addition led to the cycloadduct with no barrier. Alternatively, the reactive orientation can be achieved if one of the cyclo- butadienes undergoes valence isomerization, which is known to have a barrier of 8-10 kcal m~l-'.~' Another optimized edge-to-face supermolecule dimer, 16d, with an anti arrange-ment, is 0.8 kcal mol-' lower in energy than 16c.These lie on a very flat region of the potential-energy surface, where many dimer configurations are of equal energy. The eight-electron/eight-orbitalCASSCF calculations with the 3-21G basis set predict symmetrical stationary points 19 and 20 which are related to the anti and syn dimerization of cyclobutadiene, respectively. The energies of the anti struc- ture 19 and the syn structure 20 are 12 kcal mol-' above and 4 kcal mo1-' below that of the reactants. However, with the 6-31G* basis set, the energy of structure 20 is 7 kcal mol-' above that of the reactants. Structure 19 has the two reacting CB moieties in localized rectangular structures, but this syn- chronous concerted anti dimerization transition structure has two imaginary frequencies, one corresponding to the mode along the concerted [4 + 23 addition reaction path and the other (8% cm- ') corresponding to distortion to an asynchro- nous cycloaddition pathway.A transition structure search J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 without any symmetry constraints led to an authentic tran- sition structure, 22, with one imaginary frequency. This tran- sition structure predicts that CC bond formation is asynchronous, with one bond 0.23 and 0.61 A shorter at the 3-21G and 6-31G* levels, respectively. The 3-21G imaginary frequency mode of 22 corresponds to the formation of two CC bonds leading to the anti-tricyclic product rather than to a biradical intermediate. However, CASSCF calculations with the 6-31G* basis set give a mare asynchronous tran- sition structure, most likely leading to a biradical interme- diate.In the cyclobutadiene dimerization, synchronous and asynchronous structures are of essentially identical energy. This is a manifestation of the reactive biradical nature of cyclobutadiene: there is no advantage to maintenance of a closed-shell structure, in contrast to normal or aromatic dienes. The biradical intermediate is much lower in energy than the reactants, and the transition state has much biradical character. The CASSCF/6-31G* syn saddle point, 20, has D,, sym-metry and a loose structure with the two interacting CBs 2.45 A apart. A search for the syn dimerization transition struc- ture without any symmetry constraints was carried out start- ing from this stationary point.This led to the authentic transition structure 21, but this corresponds to the transition structure of the degenerate Cope rearrangement of the syn tricyclic product. The calculated reaction barrier from dimer 17 to 21 is 30 kcal mo1-' at the CASSCF/3-21G level, and 22 kcal mol-' at the MP2/6-31G* level. A degenerate Cope rearrangement has not yet been observed in 17 because it undergoes a forbidden electrocyclic ring opening to cyclo- octatetraene under thermal conditions.16 Stationary point 20 which appears to be a dimerization transition state, has two degenerate modes with imaginary frequencies; these lead to four possible ways of syn dimer-ization, shown with the heavy arrows in Fig.10. Any linear combination of these two degenerate modes is also possible. For example, downhill passage to 21 is also possible in four different ways, as indicated by the dotted arrows in Fig. 10. Here, collapse of 20 to 21 can occur, with subsequent collapse of transition state 21 to 17 in two different ways. Indeed, from 20 to any other points on the surface around the perimeter of the diagram in Fig. 10 is a downhill process, although the curvature in the direction of 17 is steepest. This reaction constitutes a special case where the attractive interactions between two cyclobutadienes are so large that they react without activation and end up on the surface for the degenerate Cope rearrangement (Fig. 10). The dimer- 21 ..,-_-* v17v,,17 17 ization is not required to proceed uia either 20 or 21.The reaction can bypass these stationary points in the downhill formation of stable products. The high biradical character of cyclobutadiene itself permits facile formation of biradical intermediates. Forma- tion of both singlet and triplet biradicals from two cyclo- butadienes was found to be very exothermic. The failure to locate either an asynchronous saddle point or a singlet biradical intermediate for the syn addition suggests that the syn dimerization is spontaneous without any reaction barrier when two cyclobutadienes approach each other in a stag-gered face-to-face orientation. The Cope transition structure 21 is much lower in energy than two CBs, and two cyclo- butadienes may fall into the Cope transition structure on the dimerizat ion path way.The dimerization reaction of cyclobutadiene represents an extreme of reactivity which leads to a negative energy of concert. That is, there is no advantage whatsoever to the syn- chronous concerted reaction and formation of one bond or two may happen with equal ease. Conclusion This paper has described theoretical studies of three different Diels-Alder reactions, ranging from one with no advantage to concert, the cyclobutadiene dimerization, to the reaction of butadiene plus ethene, which has an energy of concert of ca. 6 kcal mol-'. The results are generally in accord with experi- ment. The power of modern theory to evaluate closed-shell and diradical species in a balanced way is also demonstrated.We acknowledge the financial support of the National Science Foundation and conversations with Professors W. L. Jorgensen and W. Thatcher-Borden. References 1 K. N. Houk, Y. Li and J. D. Evanseck, Angew. Chem., Int. Ed. Engl., 1992,31, 682. 2 W. T. Borden, K. N. Houk and R. J. Loncharich, Am. Reu. Phys. Chem., 1988,39,213. 3 (a) K. N. Houk, J. Gonzalez and Y. Li, submitted for pub- lication; (b) however, note M. s.J. Dewar and C. Jie, Acc. Chem. Res., 1992,25, 537. 4 Y.Li and K. N. Houk, J.Am. Chem. SOC., in the press. 5 W. V. E. Doering, W. R. Roth, R. Breuckmann, L. Figge, H-W. Lennartz, W-D. Fessner and H. Prinzbach, Chem. Bet., 1988, 121, 1. 6 Y. Li and K.N. Houk, submitted for publication. 7 (a) M. Dupuis, D. Spangler and J. J. Wendoloski, GAMESS, Program QCOl, National Resource for Computations in Chem- istry Software Catalog, University of California, Berkeley, CA, 1980; (b) M. W. Schmidt, K. K. Baldridge, J. A. Boatz, J. H. Jensen, S. Koseki, M. S. Gordon, K. A. Nguyen, T. L. Windus and S. T. Elbert, QCPE Bull., 1990,10,52. 8 (a)P. Pulay and T. P. Hamilton, J. Chem. Phys., 1988,88,4926; (b)H. Yu and J. D. Goddard, J. Mol. Struct. (Theochem), 1991, 233, 129. 9 (a) F. Bernardi, A. Bottoni, M. J. Field, M. F. Guest, I. H. Hillier, M. A. Robb and A. Venturini, J. Am. Chem. SOC., 1988, 110, 3050; (b) F. Bernardi, A. Bottoni, M. A. Robb, M. J. Field, I. H. Hillier and M. F. Guest, J.Chem. SOC., Chem. Commun., 1985,1051. 10 (a) C. Doubleday Jr., M. Page and J. W. McIver Jr., J. Mol. Struct. (Theochem), 1988, 163, 331; (b) C. Doubleday Jr, R. N. Camp, H. F. King, J. W. McIver Jr, D. Mullally and M. Page, J. Am. Chem. SOC., 1984, 106, 447; (c) F. Bernardi, A. Bottoni, P. Celani, M. Olivucci, M. A. Robb and A. Venturini, Chem. Phys. Lett., 1992, 192, 229. Fig. 10 Potential-surface features in the region of syn dimerization. 11 (a) J. Storer, L. Raimondi and K. N. Houk, submitted for 20 has degenerate negative force constants, and the four Cope publication; (b) J. J. Gajewski, K. B. Peterson, J. R. Kage and Y. rearrangement transition structures (21), and four stable dimers (17) C. J. Huang, J. Am. Chem.SOC.,1989, 111, 9078; (c) M. Taage- are all lower in energy. pera and E. R. Thornton, J. Am. Chem. SOC., 1972,94,1168. 1604 12 F. G. Klarner and B. Krawczyk, unpublished results. 13 W. L. Jorgensen, D. Lim and J. F. Blake, J. Am. Chem. SOC., 1993,115,2936. 14 M. J. S. Dewar, S. Olivella and J. J. P. Stewart, J. Am. Chem. SOC.,1986,108, 5771. 15 (a) P. Carsky, R. J. Bartlett, G. Fitzgerald, J. Noga and V. Spirko, J. Chem. Phys., 1988, 89, 3008 and references therein; W. T. Borden, E. R. Davidson and P. Hart, J. Am. Chem. SOC., 1978, 100, 388; (b) For a recent experimental study, see: B. R. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Arnold, J. G. Radziszewski, A. Campion, S. S. Perry and J. Michl, J. Am. Chem. SOC.,1991,113,692. 16 (a) H. M. Frey, H-D. Martin and M. Hekman, J. Chem. Soc., Chem. Commun., 1975, 204; (b) R. S. Case, M. J. S. Dewar, S. Kirschner, R. Pettit and W. Slegir, J. Am. Chem. SOC.,1975, 204; (b) R. S. Case, M. J. S.Dewar, S. Kirschner, R. Pettit and W. Slegir, J. Am. Chem. SOC., 1975,%, 7581. Paper 3/05254K;Received 31st August, 1993

ISSN:0956-5000    

DOI:10.1039/FT9949001599

出版商:RSC    

年代:1994

数据来源: RSC

摘要:

J. CHEM. SOC. FARADAY TRANS., 1994,90(12), 1605-1616 General Discussion Prof. Shaik opened the discussion of Prof. Schleyer’s paper : (1) Is the magnetic susceptibility exaltation limited to cyclic delocalization, or would you see this phenomenon also for cases with linear delocalization? (2) Is the Li’ acceleration effect special for aromatic tran- sition states? (3) Is the acceleration correlated with the polarizability dif- ferences between transition states and ground states? Prof* SMeyer rep1ied (l) Magnetic exalta-tion does appear to be limited to cyclic delocalization. Dauben et al. examined several highly delocalized poly- methenium Of the type R2N(CH--CH)nCH=NRiwhich have essentially equal CC bond lengths. These so-called ‘linear aromatics’ showed no magnetic susceptibility exaltation.We have examined conjugated polyenyl cations and also find no exaltation. It probably would be useful to restrict the term ‘aromaticity’ to systems with cyclic delocal- ization and refer to linear and to Y-conjugation rather than ‘linear aromatics’ and ‘Y-aromatics’. (2) The Li acceleration effect is not necessarily associated + with aromatic transition states. The stereomutation of methane and the degenerate rearrangement of the atoms in acetylene is strongly accelerated by Li complexation. On + the other hand, not all aromatic transition states are stabil- ized preferentially by Li+ . The degenerate cyclic exchange involving three H, molecules is not accelerated significantly by Li+. (3) We have computed the polarizability differences between ground and transition structures in too few cases to ascertain if there is a correlation with the acceleration.I doubt if polarizability is the only effect involved. Prof. Franc1 said: If magnetic susceptibility exaltation is to be used as a signature for aromaticity, what would you recommend as a cut-off value for aromatic compounds? Some of the values presented seem very close to me. For example, cyclopentane has an exaltation of about 3, and is clearly not aromatic, while one of your aromatic examples had an exaltation of around 5. Prof. Schleyer replied: Ultimately, the answer to your ques- tion will depend on the degree of variation in the group sus- ceptibility increments as a function of structure in non-aromatic reference compounds.However, thus far we have not found differences due to strain, conformational changes etc. The ring size and number of electrons also are important. A diamagnetic susceptibility exaltation of 5 ppm cgs in a three-membered ring system probably is significant, but not in a ten-membered ring. Prof. Williams said: In your lecture you mentioned that the transition-state energy for the Cope rearrangement of semibullvalene is lowered relative to that of the reactant mol- ecule when zero-point energy effects are included in the com- putations of the Li+ complexation. As described in our paper at this Symposium, this ‘inversion’ of potential-energy sur- faces is actually observed for the radical cation derived from semibullvalene, and this is attributed to the large cationic stabilization energy that results from the reduction in ioniza- tion potential (ca.2 eV by calculation) of the neutral mol- ecule in going to the transition state. Given that the b2 HOMO of the semibullvalene transition state (Fig. 3 of my paper) is essentially a through-space combination of non-bonding allylic orbitals, can you indicate the likely extent of radical cation character introduced by Li complexation in + this favourable case? Prof-SmeYer replied: T’hank YOU for Pointing out this relationship and, in effect, calling attention, to the large changes often noted in going from hydrocarbon systems to their radical cations. This is another strategy which can be used to reduce or rearrangement barriers in peri- cyclic reactions. Nevertheless, I do not think that radical cation character of the hydrocarbon moiety contributes to the acceleration effects we observe upon Li complexation.+ As the charge on the lithium cation is nearly unity and remains so, no charge transfer is evident.Furthermore, essen- tially the same acceleration effect is computed when the lithium cation is by a point positive Prof. Houk said: You have discovered interesting new information about pericyclic transition structures, and the diamagnetic exaltation is a very interesting way to confirm and quantify the aromaticity of these species. I have related questions about the calculated chemical shifts in the transition structures.(1)You note the upfield shifts of the hydrogens ‘inside’ the Diels-Alder and hexatriene electrocyclic transition states. Perhaps coincidentally, we calculate anomalously high sec-ondary deuterium isotope effects for these same hydrogens in these transition structures. This indicates high bending HCC force constants for these hydrogens due to steric crowding. Could this influence their chemical shifts? (2) In Mobius aromatic transition states, such as cyclo-butene openings and octatetraene cyclizations, there is for- mally no difference between the top and bottom of the .n cloud. Will this influence the ring-current effects? Have you calculated chemical shifts for protons in transition states of pericyclic transition structures involving Mobius aromatic systems? Prof.Schleyer replied: (1) This is an interesting analogy, but I doubt if the same effects which result in anomalously high secondary deuterium isotope effects are responsible for the upfield chemical shifts we compute. Crowding may influ- ence chemical shifts, but to a lesser extent. We find pro- nounced upfield proton chemical shifts in cases where no crowded environments are involved. (2) The Mobius transition structures we have investigated had C, symmetry (i.e. both sides are the same), but the ring- current effects (magnetic susceptibility exaltation and dis- placement of the hydrogen chemical shifts) are quite pronounced. The existence of a ring current in an electron- delocalized cycle is important, whatever the overall symmetry of the species may be.Dr. Reynolds said: In the light of your comment that rate acceleration of hydrocarbon reactions by Li is not observed + experimentally because of the lack of a suitable medium for Li+, could you comment on whether you have investigated methods for including the solvent and, if not, could you also predict how you would expect such calculations to affect your results? Prof. Scbleyer replied: The simplest method to investigate solvation effects would be to complex the Li+ with one or more model solvent molecules. Alternatively, continuum models can be employed (self-consistent reaction field, SCRF) or a combination of the two. Actually, we have been aiming to find large influences, rather than ways to attenuate them! Since Li+ binds moderately strongly to unsaturated hydro- carbon substrates, acceleration effects might be observable in the gas phase or in saturated hydrocarbon solvents with a very weakly binding gegenanion.Perhaps the large electro- static fields in zeolites would function similarly. Our findings are quite new, and practical applications have not yet been explored. Dr. Mitchell said: The ability of Li+ to lower the energy of a transition state is of interest in relation to the possible cata- lytic behaviour of Lif and other cations acting as Lewis acids. It was not clear, however, from your presentation whether Li’ was merely a probe for aromatic character in the transition state or whether Li’ was inducing aromaticity.It would also be helpful to know if the lowering of the activa- tion energy was due to interaction of the transition state with the Li+ or to the induction of aromaticity. Do Li’, and other cations, also lower the energy of non-aromatic transition states? Prof. Schleyer replied: We have examined the Li+ acceler- ating effect with a set of model calculations. If Li+ is replaced by a point charge, the energy difference between ground and transition state remains essentially the same. This also is true, if the charge plus the lithium orbitals (i.e. the basis set expan- sion of the Li-less systems) are both employed. However, the lithium orbitals alone have very little effect relative to the parent hydrocarbon systems.The magnetic susceptibility exaltation of the transition structure is nearly the same whether or not Li+ is present; hence, I do not think Li+ acts primarily to induce or increase aromaticity, although there is some change in the geometries. The problem in studying antiaromatic transition structures is that they cannot be located properly computationally. By imposing symmetry, stationary points might be found, but these have a higher order (more than one imaginary frequency) and are not true transition structures. However, we have computed some remarkably large Li accelerations,+ e.g. for rearrangements in which aromatic transition states are not involved. Prof. Borden said: You have said that ‘aromatic’ transition states are polarizable and also have large diamagnetic ring currents.However, polarizabilities increase with the proxim- ity of filled and unfilled orbitals, as do paramagnetic ring cur- rents, provided that the filled and unfilled orbitals can be mixed by a magnetic field. Is the resolution of the apparent paradox that you have presented that in aromatic transition states the proximate filled and unfilled orbitals have the wrong symmetry to be mixed by a magnetic field? I suspect this to be the case. Since they have different numbers of nodes, mixing the filled and empty orbitals in an aromatic system does not give rise to orbital angular momentum and, hence, does not give rise to paramagnetic ring currents.Prof. Schleyer replied: Although we have carried out pol- arizability calculations which do indicate transition states to be more polarizable than ground states, we do not know if this effect is sufficiently large to account for the Li+ electro- static accelerations. Your thoughtful comment needs further GENERAL DISCUSSION examination. The IGLO program does provide a break-down of the total magnetic susceptibility into diamagnetic, para- magnetic (as well as non-local) contributions. In the systems we have examined, the paramagnetic contributions generally are small, but there are some exceptions. Prof. Kutzelnigg and his group have considered these contributions in detail in some cases, but we have not carried out a systematic analysis at Erlangen. Prof.Shaik communicated: I note with much interest that what you so invincibly showed is that the magnetic suscepti- bility exaltation is a mark of the topology of electronic de- localization: the topology that we call ‘aromatic’. At the same time your analysis showed that this property belongs to stable molecules as well as to transition states. Do you observe any dependence of the exaltation on the stability of the ‘aromatic’ species, namely, whether it is a transition state or a stable ground state? Prof. Schleyer replied:The diamagnetic susceptibility exal- tation is known to depend on the number of delocalized elec- trons as well as the radius of the ‘ring-current’ cycle. It should also depend on the ‘degree’ of delocalization, but it does not seem to matter whether a ground state or a tran- sition state is involved.Several electrocyclic transitions structures we have exam- ined have diamagnetic susceptibility exaltations somewhat greater than those of benzene. In a collaborative study with Prof. Peter Freeman (who was a sabbatical-year guest at Erlangen), we have analysed the aromaticity/antiaromaticityin five-membered ring carbo- cycles (C,Hf and C,H,), and a number of heterocyclic ana- logues. The aromatic stabilization energies were evaluated by using appropriate five-membered ring reference compounds. We find a remarkably linear relationship between these aro-matic stabilization energies and the magnetic susceptibility exaltation, both diamagnetic (for the aromatic species) and paramagnetic (for the antiaromatic systems).While it may be premature to generalize these findings, they suggest that it may be possible to develop suceptibility exaltations into a quantitative measure of cyclic delocalization. Of course, such electron delocalization is only one of the energy contributions. Thus, one cannot expect a correlation between the diamagnetic susceptibility exaltation and e.g. the degree of concert of a pericyclic process when ‘strain’ and steric factors are important. Prof. Michl communicated: Qualitatively, I would guess that the extra polarizability in an aromatic transition state appears in the ‘aromatic plane’, which is not where the Li’ ion or the extra positive charge was located in most of the calculations you have told us about.This suggests that even larger effects might be predicted at other geometries, with the positive charge in this ‘plane’. I wonder whether the non-uniform nature of a central field is important and whether it would be useful to calculate the polarizability tensor for the transition state, i.e. look at the energy change in a uniform electric field and predict changes in the activation energy from that. Prof.Schleyer replied:These are interesting suggestions for further investigation. In my lecture, I attributed electrostatic acceleration by Li+ to the greater polarizability of the tran- sitions state over the ground state. While we have carried out a few polarizability computations which confirm this assump- tion, we have not yet attempted to assess the magnitude of GENERAL DISCUSSION the polarizability or other effects or to analyse them in greater detail.The greater binding energies of Li’ to TSs over GSs may be due to the larger number of contacts or to the greater average effectiveness of the interactions in the TS, when the coordination remains the same. We have generally employed optimized geometries in our work, but have also carried out model computations along the lines of your question. Moving the Lif out, away from the equilibrium position, results in a smaller acceleration. Conversely, moving Li in towards the ‘aromatic plane’ + results in a greater effect. (The shielding effect on the chemical shift also responds similarly and is largest in the centre of the ring.) Using equilibrium geometries, a greater acceleration results if Li’ is replaced by Be2+, a small dication. Dr.Quapp said: My comment concerns the first topic of Prof. Schlegel’s paper, the bifurcation of reaction paths. With the steepest-descent path’ (SDP) dx -= -grad E(x)dt we cannot describe, in principle, bifurcations outside of stationary points. The system of equation is an autonomous differential equation system, which has outside of stationary points grad E # 0 definite solutions, thus it cannot admit bifurcations. If a reaction path bifurcates along a slope on the PES, this cannot be described with the mathematical tool of a gradient system.We need the more complicated tool of gradient extremals (GE).’ Curves running along a valley floor path, or along a ridge, are GE. They cross a level line at that point where the slope of the gradient is extremal. Thus, a GE probes the extremal curvature of the level lines3 Surprisingly, the GE differ from SDPs. They are isolated curves, because they are solutions of (N-1) equations between the N indepen-dent coordinates. This is also contrary to the definition of SDPs given above. I will give three examples in analogy to Fig. 1 of Prof. Schlegel’s paper; and I will explain the behaviour of the test potentials near a bifurcation point. A surface linear in y and -2 -1 0 1 2 Fig. 1 The test potential x4 + x2y represents a special monkey saddle where one valley ground path and the opposite ridge are flat lines (the vertical centre line).Zero point (0, 0) is the valley-ridge inflection point (VRI) where the gradient extremals also meet. The dashed curves are ridges and the bold curves are valley ground lines. quartic in x is F(x, y) = x2(x2 + y) It is a special monkey saddle with a flat valley and a flat ridge in the opposite direction. The 2D gradient extremal condition is: Thus GE(~,y) = 2x3(-x2 -8x4 + 2y2) = o Its solution is (see Fig. 1) {Yl(X) = x JC(1 + 8x2)/21 Y2(4 = x JC(1 + 8x2)/21 x = 0, thus y3(x)= (y -axis)} The zero point (0, 0) is the valley-ridge inflection point. It is also the bifurcation point of the three valley grounds (bold curves) and three ridges (dashed curves) of this potential.A second surface, also linear in y and quartic in x, is the following: F(x, y) = y + x2(x2+ y) The 2D gradient extremal condition gives: GE(x, y) = 2x[(1 + 2x2 + 25x4 + 8x6) + 16x2y + 2(1 -x2)y2] = 0 Its solution is (with an apparent singularity at x = fl), 8x2 + (1 + x2)J2J( -1 + x2 + 8x4)Yl(4 = 2(-1 + xK1 + x) 8x2 -(1 + x2)J2J( -1 + x2 + 8x4) Y2(4 = 2(-1 + xX1 + X) x = 0; thus y3(x)= (y -axis) given in Fig. 2. Along the three gradient extremal curves their character is changed: y3(x) is composed of a valley ground (bold) and a ridge (dashed). The two pieces are divided by the valley-ridge inflection point (cross). The other two branches yl(x) and y2(x)are also composed of two different curves: The bold parts y2(x) are again the valley grounds of the two side valleys.They end in a turning point; and the curves continue as flank lines yl(x) (dot-dashed), dividing the corre- sponding valleys from the ridge. There is no connection between the three bold curves, which are the reaction paths, if we understand the valley ground as the reaction pathway. All the valley ground curves are continuable, but the continuation is different : one ridge, characterized by passing the valley ridge inflection point, and two flank lines, on the other hand. I think this figure is similar to the test potential of Fig. 1 of the paper of Prof. Schlegel. If there is no connection between the three valley floor curves, then this connection cannot be found by any special SDP either.Of course, the gradient of the surface is non-zero, outside the zero point (0, 0). Hence, we can go up or go down in the gradient direction starting from any point of the surface. In Fig. 3, a steepest ascent, starting in T, is given by bold arrows about the gradi- ent field. In comparison an SDP is also drawn starting near the zero point. The two paths do not meet. The existence of turning points, and their role for understanding the valley ridge structure of a surface, mare discussed in ref. 4, see also a proposal.’ GENERAL DISCUSSION -2 -1 0 1 2 Fig. 2 Test potential x4 + x2y + y with gradient extremals without a bifurcation point. The straight centre line, downhill in potential (bold), is a valley ground path which meets the valley-ridge inflection point (VRI) at (0,O)and continues to the ridge (dashed).Dot-dashed curves are flank lines between the ridge and the two valleys. There is no bifurcation point between the three (bold) floor lines. Flank lines and ground paths meet together in two turning points (T) where the flanks and the grounds end. A third test surface, linear in y and quartic in x, is F(x, y) = -y + x2(x2+ y) Here, we find two saddle points. The 2D gradient extremal condition gives : GE(x, y) = 2~[(-1 + 2x2 + 23x4 -8x6) + 16~ + 2(1 + x2)y2] = 0 Its solution is a set of three crossing curves, given in Fig. 4: -8x2 + (1 -x2),/2,/(1 + x2 + 8x4) {Yl(X) = 2(1 + x2) -8x2 -(1 -x2),/2,/(1 + x2 + 8x4) Y2(4 = 2(1 + x2) x = 0; thus y3(x)= (y -axis)) Again, the zero (0, 0) is the valley-ridge inflection point.However, the bifurcation point (B,) of the three valleys is 0.5* 0. -0.5 * -1.0 * -1.5 . -1.0 -0.5 0 0.5 1.o Fig. 3 Enlargement of the region between the turning points (T) and VRI of Fig. 2 with level lines and the gradient field. The bold arrows give a steepest descent and a steepest-ascent path. c 0-.-1 -2. -3 -I. -2 -1 0 1 2 Fig. 4 Test potential x4 + x2y -y with gradient extremals of differ- ent types Bold curves are valley ground paths. The dashed curves are ridges. The valley-ridge inflection point (VRI) at (0, 0) is not the bifurcation point (B,) of the three ground lines, and it is not the bifurcation point (B,) of the three ridge/flank lines.Ridges and ground paths meet in the two saddle points. shifted downhill, and the bifurcation point (B2)of the other branches yl(x) is shifted uphill. Ridges and valleys meet in two saddle points (SP).The behaviour of the three ridges is further disturbed by saddle points which are between the central ridge and the two side ridges. After passing one of the SPs from outside, we find a small piece of a ridge. However, ~~ then a very flat turning point (T) emerges, and the curve of the GE continues as a flank line up to B, . The message of Fig. 1-4 is the following: Bifurcation points can be defined and we can calculate bifurcation points of valley floors (at least on simple test potentials).However, in the theory of GE curves, the valley-ridge inflection point (VRI) and the bifurcation points (B) may be different points. 1 W. Quapp and D. Heidrich, Theor. Chim. Acta, 1984,66,245. 2 D. K. Hoffman, R. S. Nord and K. Ruedenberg, Theor. Chim. Acta, 1986,69, 265. 3 D. Heidrich, W. Kliesch and W. Quapp, Properties of Chemically Interesting Potential Energy Surfaces, Lecture Notes in Chem- istry, Vol. 56, Springer, Berlin, 1991. 4 W. Quapp, Theor. Chim. Acta, 1989,75,447. 5 M. V. Basilevski, Chern. Phys., 1982,67,337. Prof. Truhlar commented (in part communicated) : It was stated in one of the discussion remarks that an imaginary frequency in one of the modes orthogonal to the reaction path signals a reaction-path bifurcation.This is not true. First of all as already stated in Prof. Schlegel's paper and in the remarks by Dr. Quapp, the steepest-descent path, as a mathematical entity, cannot bifurcate. In actual calculations the steepest-descent path would follow the ridge at a valley- ridge inflection (VRI) point,' except for the tendency of round-off error to push it to one side or the other. Further- more, an imaginary frequency orthogonal to the reaction coordinate should not always be considered to be a signal of a physically significant valley-ridge transition. Rather it may often signal a valley-ridge inflection point in non-physical coordinates of a system that is best thought of as residing in a single valley in more physical coordinates. This state of affairs is temporarily disorienting to many researchers because we are all so used to calculating frequencies at GENERAL DISCUSSION stationary points (equilibrium structures, saddle points, .. .) where the frequencies are independent of the choice of coor- dinates, e.g. they are the same in internal coordinates (bond stretches, bond angles, dihedral angles, ...) as in Cartesian coordinates. But this invariance does not hold at non-stationary points along a reaction path because the gradient does not vanish. These issues are discussed in detail in a 1991 paper in the Journal of Chemical Physics.2 Let me state a related central issue: Every VRI point does not signal a case where there are two products (i.e. two local minima), with a ridge between them.Non-physical VRI points may occur even when the reaction path leads straight to a single product. 1 See, e.g. B. C. Garrett, D. G. Truhlar, A. F. Wagner and T. H. Dunning Jr., J. Chem. Phys., 1983,78,4400. 2 G. A. Natanson, B. C. Garrett, T. N. Truong, T. Joseph and D. G. Truhlar, J. Chem. Phys., 1991,94,7875. Prof. Schlegel replied: The correct terminology was used in the paper. The question of coordinate systems is an impor- tant one. Only the stationary points are invariant to a change in coordinate system. The steepest-descent path, and hence the valley-ridge inflection points depend on the choice of coordinate system. Dr. Stacho said: Let c be a smooth curve such that the energy function E has a local minimum at any point of c on the hyperplane, orthogonal to the tangent vector of c.Then the tangent vector must necessarily be parallel to the gradient of E. (Thus in this sense minimal energy paths are automati- cally steepest-descent/ascnt paths.) It follows from the Hartman-robman theorem that if c ends in a stationary point p with a non-degenerate Hessian then the tangent vector of c at the point p is an eigenvector of the Hessian (of E). Thus, in most cases, bifurcations of the reaction path are orthogonal,similar to our example 3.5 in ref. 1. Could you treat our function with your method? 1 M. I. Ban, Theor. Chim. Acta, 1992,83,433. Prof. Schlegel replied :Our methods for following reaction paths can in principle be applied to any continuous potential- energy surface.As already stated by a number of authors, true bifurcations of reaction paths occur only at stationary points, and, at stationary points, reaction paths are orthog- onal. Dr. Quapp said: In response to the question of Prof. Schle- gel about the Muller-Brown Potential,’ a gradient extremal (GE) of this potential, see Fig. 5,2 is a nice example showing the action of the definition of these curves. The bowl of Min 1 is a deep, long and relatively straight valley. In contrast, the SP 1 looks like a ‘swallows nest’ at its height. The col of SP 1 opens to the main valley, and a steepest-descent path perpen- dicularly goes downhill to the level lines of the hollow ground. At the floor it joins the floor line.However, nowhere on the floor line can we decide a point of line crossing because this is an asymptotic join. The GE curve, on the other hand, shows totally different behaviour. It also runs along the col of SP 1, but then it shears off and goes on uphill! Very strange? No, this behav- iour is a clear consequence of its definition, to mirror the existence of a valley floor curve: the col of SP 1 ends at the slope of the greater valley of Min 1. Thus, the GE of the valley also has to end. Its end point is then a turning point (T). The curve continues as a flank line of the potential. 1,. , , , , , , .-, , , , , , , , , , , . ~, 2 -1 0 1 Fig. 5 Solid lines are level lines and the special steepest-descent curves connecting the stationary points, and bold faced curves are gradient extremals on the Miiller-Brown test potential, see also ref.3. T is a turning point of a GE curve. Note: Between the left deep minimum and the next saddle point SP 1 there is no connection by a gradient extremal ! 1 K. Muller and L. D. Brown, Theor.Chim. Acta, 1979,53,75. 2 0.Imig, Diplomarbeit, Fachbereich Chemie, Universitat Leipzig, 1993. 3 J-Q. Sun and K. Ruedenberg, J. Chem. Phys., 1993,98,9707. Prof. Schlegel commented : Steepest-descent paths and gradient extremals are both useful tools for exploring potential-energy surfaces. The properties of steepest-descent paths are well known. Gradient extremals have some satisfac- tory properties, They pass through stationary points, they are locally defined and they can handle some types of bifurcation, as discussed by Dr.Quapp. However, gradient extremals show some unsatisfactory behaviour. They do not necessarily connect a saddle point and nearby minima. Gradient ex-tremals can have turning points (they can change direction from downhill to uphill or vice versa) and can have discontin- uities (see Fig. 5 of Dr. Quapp’s comment). If the intent is to model the behaviour of a reaction on the potential-energy surface, it is perhaps better to avoid the idiosyncracies of gradient extremals and tolerate the few limitations of steepest-descent reaction paths. Prof. Karplus said: My question is for both Prof. Schlegel and Dr. McDouall. The Elber algorithm was developed to determine relatively crude reaction paths for complex systems with lo00 or more of degrees of freedom and we have found it useful in some applications.I was interested to see how well it works for small systems and am curious about the time required rela- tive to that of the more standard approach of Prof. Schlegel. Conversely, I am curious to know whether Prof. Schlegel could indicate whether his approach can be extended to large systems (like proteins). Also, I should like to mention that we have been concerned with finding true saddle points for large systems and have developed a method for doing so in large systems.’ This has been tested in model systems such as the Muller-Brown potential. 1 S. Fischer and M. Karplus, Chem. Phys. Lett., 1992,194,252.1610 Prof. Schlegel replied: The methods currently used for small molecules for finding minima, transition states, reaction paths and conical intersections have been reviewed recently.’ For macromolecules, there can be many minima of similar energy, many comparable transition states and numerous reaction paths. Statistical and dynamical methods are prob- ably the best current approaches for such high-dimensional sys tems. 1 H. B. Schlegel, Geometry Optimization as Potential Energy Sur- facer, in Modern Electronic Structure Theory, ed. D. R.Yarkony, World Scientific, Singapore, 1994. Dr. McDouall also replied to Prof. Karplus: We are aware of the conjugate-peak-refinement approach of Prof. Karplus and co-workers.Our intention in the present work was to obtain a method which would give reasonably accurate reac- tion paths over which we could follow the evolution of various molecular properties. More accurate saddle-point location was not a major concern. I believe the ‘Elber-Karplus-type’ approach that we have adapted, and others are looking at, has a major role to play in future studies of reaction paths for large molecular systems, where traditional methods become impracticable. Dr. Nguyen said :When exploring potential-energy surfaces and/or characterizing transition structures, we often encoun- ter branching points, in particular when the TS has no sym- metry and/or the product possesses two distinct conformations. We know that these non-stationary points exist only in a certain formalism; a true steepest-descent path does not bifurcate.Nevertheless, for both practical and edu- cational purposes, it seems to me useful if we could somehow ‘define’ those points. Some years ago, Baker and Gill2 attempted to do that and proposed an algorithm to locate branching points. Accordingly, a branching point is a point where the eigenvalue of the Hessians perpendicular to the reaction coordinate vanishes. Would you comment on this view? 1 S. Malone, A. F. Hegarty and M. T. Nguyen, J. Chem. SOC., Perkin Trans. 2, 1988,477. 2 J. Baker and P. M. W.Gill, J. Comput., Chem., 1988,9,465. Prof. Schlegel replied: As already pointed out by Rueden- berg, and reiterated here by myself and by Prof.Truhlar, the point on a reaction path where the Hessian perpendicular to the path has a zero eigenvalue should be termed a valley- ridge inflection point, not a ‘branching point’. Indeed these points have topological significance for the connectivity between various stationary points, but it is incorrect to draw a steepest-descent reaction path as bifurcating at the valley- ridge inflection point. Prof. Ban asked: (1) What kind of improvement can be expected in the results if we apply your method of higher order in comparison with your lower-order calculations? (2) What are the convergence criteria of your methods? Prof. Schlegel replied: I am hoping for an improvement of up to a factor of five in the step size for the explicit fourth- order methods, when compared to other explicit second- order methods.The comparison in cost with our implicit second-order method is difficult to estimate because the latter involves an optimization but no Hessian calculations. We have recently found that the convergence criteria for our second-order implicit method must be tightened considerably GENERAL DISCUSSION to obtain accurate projected frequencies in the immediate vicinity of the transition state. Dr. Stone said to Dr. McDouall: It seems to me that a more suitable functional would be obtained by omitting the factor of 1/L in eqn. (1). The functional given is the average energy along the path, and can be made arbitrarily close to the minimum energy by choosing a path which follows an arbitrarily long and convoluted trajectory near the minimum.This deficiency in the formal definition is related to, but is not the same as, the problem experienced by the authors in for- mulating their numerical approximation to the functional. Dr. McDouall replied: You make a valid comment regard- ing the term in eqn. (1). Leaving this term out will certainly avoid the possibility of generating an arbitrarily long path. A preferable alternative in my view would be to replace 1/L by 1/M (where M is the number of grid points). In this case eqn. (1) will still represent the average value of the grid points (though not of the path). Prof. Tomasi said: This definition of reaction path appar- ently depends upon the choice of the coordinate.I would like to know if you have any experience of the effect of passing, for example, from Cartesian coordinates to mass-weighted coordinates. Dr. McDouall replied: We have not looked at the use of mass-weighted coordinates. Our main concern was to obtain the minimum-energy path on the surface rather than to obtain the detailed atomic displacements during a reaction. To study the latter we would certainly need to use mass- weighted coordinates. Prof. Shaik said: I am trying to understand the bifurcation problem in chemical terms. Is it true that the addition of HF (HX in general) to C2H, will have a bifurcation point, sup- posedly because it leads to two conformers 1 and 2? If so, then a lot of reactions will possess this bifurcation, e.g.when two enantiomers lose their optical activity. How did you resolve, in the past, the bifurcation problem in the case of HF + C2H,? H H H H 1 2 Prof. Schlegel replied: The reaction HF + C2H, has a sta- tionary point with HF hydrogen-bonded to the n system. F ‘c=cO H‘ ’H At a stationary point, a reaction path can bifurcate’ and the paths lead to fluorine adding to either carbon. In the more general case there will be a valley-ridge inflection point before the transition states rather than an intermediate. To a first approximation for these surfaces, the branching ratio for GENERAL DISCUSSION the formation of the products will be determined by the two transition states rather than by the path bifurcation on the valley-ridge inflection point.The situation where the valley- ridge inflection point lies beyond the transition state is more complicated, and it is the detailed dynamics on the surface that will determine the branching ratio. 1 K. Ruedenberg et al., Theor. Chim. Acta, 1986,69,281. Dr. Stacho said: What can be stated about the numerical stability of your methods? Your paper stated that none of your methods could handle the case with a Fresnel spiral- shaped reaction path. What was the reason? What was the definition of the energy function in this case? Prof. Schlegel replied: Based on the tests with the logarithi- mic spiral valley (Fig. 6 of our paper), our fourth-order explicit method 2 has about the same stability as our second- order implicit methods, and both are more stable than the LQA second-order explicit method.A more detailed assess- ment of the methods will be made once they are incorporated in the electronic structure codes. No single-valued two-dimensional surface was constructed for the Fresnel spiral because the logarithmic spiral incorporates the essential fea- tures (curvature changing monotonically with the reaction path). A three-dimensional Fresnel spiral could be con-structed in the same fashion as the helical valley, but the mathematical form would be rather complicated because of the nature of the Fresnel integrals. Dr. Stacho (communicated): In all of the examples given so far, the reaction path is a curve tangential to the gradient field of the energy function and whose tangent vectors are Hessian eigenvectors.The space transformation-invariant Jasien-Shepard reaction path concept is defined in terms of vector field dynamics of slightly more general type than that of gradient fields. With what modifications can your methods be applied to follow reaction paths in dynamical systems defined by general vector fields? How can your explicit methods be used to treat orthogonal bifurcations? In particu- lar, how can they be applied to determine the reaction paths of the model function given in ref. 1. 1 L. L. Stacho and M. I. Ban, Theor. Chim. Acta, 1993,84,536. Prof. Schlegel replied: Most reaction path following methods depend only on the gradient, and thus should be applicable to functions defined only as vector fields.Orthog- onal bifurcations occur at stationary points. Any reaction path following method can be used to follow a path from a first-order saddle point down to a stationary point. If this stationary point is also a first-order saddle point, then the reaction path following method can be used to follow the path downhill in both directions. Your surface is an example of the case where the path from one first-order saddle point descends to another first-order saddle point. Prof. Karplus said: I am curious to know what work, if any, has been done to analyse the dynamics on a bifurcated surface (e.g. one that is asymmetric). Near the bifurcation, there is presumably a very low barrier in a direction approx- imately perpendicular to the reaction coordinate.This could cause rather complex dynamics. Prof. Schlegel replied : Dynamics on bifurcating surfaces have been discussed by Krauss and De Pristo.’ There are probably also more recent references. 1 W. A. Krauss and A. E. De Pristo, Theor. Chim. Acta, 1986, 69, 309. Prof. Truhlar also replied: The dynamical behaviour when a minimum-energy path is a ridge depends strongly on the system and the energy. In the vicinity of a valley-ridge inflec- tion point, the ridge will be only a little higher in energy than the dual valleys it separates, and in such a case the system will typically pass easily between the valleys. Ridges that are higher compared to the available energy can isolate a system on one side or another.Dr. van Duijnen said: In my experience most continuum SCRF approaches use cavities which are too small, i.e. they place source charges too close to the boundary. This is irre- spective of the form of the cavity. Changing the size of the cavity, e.g. by taking different atomic radii, ‘solvation’ ener- gies may range from -co to O! Most choices for the cavity’s size are ‘intuitive’ or ‘practical’ rather than physical. (See, e.g. ref. 1, where we put (ad hoc) the boundary at least one solvent radius away, and ref. 2, where we gave physical reasons for doing so and why it is necessary to include at least one dis- crete solvation layer.) In your example CO, + OH--+HCO; the initial and final states are overwhelmingly ionic with a monopole too close to the boundary of the cavity, while the charge distribu- tion of the transition state may be diffuse, probably putting the monopole farther from the boundary.Hence, your barrier heights are too large. In this respect, the simulation with explicit solvent molecules is much better and more trust-worthy. 1 J. A. C. Rullmann and P. Th. van Duijnen, Mol. Phys., 1987, 61, 293. 2 A. H. de Vries, P. Th. van Duijnen and A. H. Juffer, Znt. J. Quantum Chem., Quantum Chem. Symp., 1993,27,451. Prof. Truhlar said: Dr. Van Duijnen has remarked on the inappropriateness of an ellipsoidal cavity for describing the progress of a reacting system along a reaction path and on the difficulty of choosing the ellipsoid boundaries.In this respect, I note that not all continuum solvation models require spherical or ellipsoidal cavities. A much better model in many cases is the assumption of a set of superimposed spheres centred at the atomic nuclei. This model has been used, for example, in SCF calculations by Tomasi and co- workers1 and Cramer and myself,2 in molecular mechanics calculations by Still et uZ.,~ and in Poisson or Poisson-Boltzmann calculations by Honig and Karplus and their co-worker~.~~’ a poster presented at this Symposium, the In Nancy group has also discussed an extension of their formu- lation to allow such more general cavities.6 With such arbitrarily shaped cavities the continuum models can better represent the solute at any point along the reaction path.The difficulty of choosing the boundary between the inside and outside of the cavity remains, but it can be alleviated in two ways, namely (i) choosing the atomic radii semiempirically, and/or (ii) including first-solvation-shell effects explicitly to make up for the inhomogeneity of the dielectric properties of the solvent in the boundary layer. Both approaches are employed in the SMx models developed by Cramer and myself.2 1 S. Miertus, E. Scrocco and J. Tomasi, Chem. Phys., 1981,55, 117. 2 C. Cramer and D. G. Truhler, J. Am. Chem. SOC., 1991,113, 8305; J. Computer-Aided Molec. Design, 1992,6,629. 3 W. C. Still, A. Tempczak, R. C. Hawley and T. Henrickson, J. Am. Chem. Soc., 1990,112,6127. 1612 4 K.A. Sharp and B. Honig, Annu. Rev. Biophys. Biophys., Chem., 1990, 19, 301. 5 D. Bashford and M. Karplus, Biochemistry, 1990, 29, 10219; C. Lim, D. Bashford, and M.Karplus, J. Phys. Chem., 1991, 95, 5610. 6 V.Dillet and S.Antonczak, poster at this Symposium; see also V. Dillet, D. Rinaldi, J. G. Angyan and J-L. Rivail, Chem. Phys. Lett., 1993, 202, 18. Dr. van Duijnen responded: My remark had more to do with the size of the cavity than with its form. Most cavities are just too small (in particular in water). Including the dis- crete first solvation layer has been our standard for many years (see, e.g. ref. 1 and 2 in my last comment). This requires some thermodynamical averaging in order to arrive at some- thing like a Gibbs energy.However, the problem of the dis- tance between this first solvation shell and the boundary with the continuum remains the same of course! Prof. Sbaik opened the disscussion on Prof. Butler’s paper: Let me see if I understood you correctly. You are saying that the C-Br cleavage is not efficient because it must involve avoided crossing (nn*-nu* type). But actually the C-Cl cleavage involves precisely the same avoided crossing, so what is the difference? Does the larger avoided crossing for C-Cl cleavage make the two barriers equal? Prof. Butler replied: While the barriers along the C-Br and C-Cl fission reaction coordinates are both formed from avoided electronic configuration crossings -~(no n*c-o-nx r~*~(X=Br, C1) (a””-a”a’)), and what you or Silver (ref.9) would call the ‘resonance energy stabilization’ or ‘barrier energy lowering’ at the avoided crossing to C-Cl fission is larger than that for C-Br fission, it is not enough of a difference to make the two barriers equal. The barrier to C-Cl fission is still about 10 kcal mol-’ higher than the barrier to C-Br fission. nhe electronic configuration inter- action matrix elements (BQ in your notation) are only 0-3 kcal and the C-Cl diabatic crossing (AE, in your notation) is more than 10 kcal mol-’ higher than the C-Br crossing, so the resulting barrier height, (EbPrrierAEc -BQ)along the = C-Cl reaction coordinate is still higher than that along the C-Br reaction coordinate.] The key difference between the C-Br and the C-Cl reaction coordinates in bromo-propionyl chloride is that the crossing is so weakly avoided along the C-Br reaction coordinate, with typical splittings (2B between the adiabats of 20 cm-’ as compared to 400 cmg! along the C-C1 reaction coordinate, that the rate con- stant for C-Br fission is dramatically reduced due to the nuclear dynamics non-adiabatically recrossing the C-Br reaction barrier.You may view this recrossing as follows: the electronic configuration interaction matrix elements between the no n*c-o and the nBr u*C--Brconfigurations are so weak that the electronic wavefunction cannot change rapidly from non*c-o to nBrn*C--Br in character as required if it is to follow the adiabatic reaction coordinate for C-Br fission.Instead, each time the molecule tries to cross the barrier to C-Br fission, the electronic wavefunction retains no n*,c-o character and the C-Br bond retains a bonding electronic configuration. The probability of retaining the no n*c-o con-figuration (which results in a ‘hop’ to the bonding region of the upper of the two adiabats at the avoided crossing) as the molecule attempts to traverse the avoided crossing can be roughly estimated from a Landau-Zener model, P,,, = ~xPC-2n(V1J2/(A IAF I UreJ = 1 -24 v12)2/(A I LWI (for small V12). Thus the reduction in the rate of the reaction is GENERAL DISCUSSION huge when V,, (or B, in your notation) is small; roughly there is a 99.95% chance that a trajectory trying to undergo C-Br fission will retain bonding character at the avoided crossing rather than adiabatically crossing the barrier and continuing to dissociation.Since V,, is much larger at the barrier to C-Cl fission, the nuclear dynamics are much more likely to cross the barrier to C-C1 fission barrier adia- batically with each try. Thus, you get the wrong prediction for the branching ratio if you consider just the relative barrier heights, as the nuclear dynamics can rarely adiabatically cross the barrier to C-Br fission. The reduction in rate con- stant due to non-adiabatic recrossing is well understood for long-distance electron-transfer reactions (ref. 7); our work here shows that it is critical for predicting the rate constants of Woodward-Hoffmann-forbidden reactions.Prof. Karplus said : From the molecular beam experiment, you have some idea of the lifetime of the excited molecule before it dissociates. Does it have many chances to try the reaction so that even if the probability of a single ‘try’ is small there might nevertheless be a significant probability for dissociation by the forbidden path. I am curious to know the orders of magnitude involved, i.e. how often does the mol- ecule try? Prof. Butler replied : The molecular beam experiments on bromopropionyl chloride and bromoacetone do give us a crude upper limit to the lifetime of the excited molecule before dissociation. Our photofragment angular distributions are highly anisotropic, so molecular rotation has not had time to smear out the anisotropic orientations of excited mol- ecules produced by photoexcitation with linearly polarized light.(The angular distribution can also be smeared by dis- tortion of the molecular frame, but we are talking about an upper limit here so will not further discuss this.) The rotation- al cooling in our particular supersonic expansion is only moderate. Roughly, the anisotropic angular distributions indicate that dissociation occurs in less than a few pico- seconds. A few picoseconds is, however, a long time for nuclear dynamics. The vibrational frequency of a C-Br stretch is of the order of 600 cm-’,so in a classical model a trajectory that has tried and failed to cross the barrier to C-Br fission adiabatically (by hopping to the upper adiabat as the bond is stretching, reaching the outer turning point of the C-Br stretch on the upper adiabat and hopping back down to the lower adiabat as the C-Br bond length decreases) might attempt to cross the barrier again in 50-60 fs in a crude approximation. Of course, the energy can drain from the C-Br reaction coordinate before the next attempt and the molecule may instead sample the region of phase space near the barrier to C-Cl fission and be lost to C-Cl fission before it has a chance to retry crossing the barrier to C-Br fission.An RRKM estimate tells us that statistical tra- jectories sample the C-Br barrier (with enough energy to surmount the barrier) heading toward products much more often than the C-Cl barrier, so it is non-adiabatic recrossing that is the cause of the rate constant for C-Br fission being smaller.We do not know the heights of the barriers to C-Br or C-Cl fission relative to the bottom of the A” potential-energy surface accurately enough to calculate a good RRKM estimate of the rate constant for C-Br and C-C1 fission in the absence of non-adiabatic recrossing. This would let me tell you how many times a picosecond the molecule would attempt to cross the C-Br and C-Cl fission reaction bar- riers, respectively. The excess energy above the C-Br reac-tion barrier is at least ca. 10 kcal mol- ’,so I would guess the GENERAL DISCUSSION molecules would have multiple tries at adiabatically crossing the barrier to C-Br fission. Of course, the probability of crossing the C-Br fission barrier adiabatically is small at every retry, but especially for bromoacetyl chloride, not negli- gible.Experimentally, although non-adiabatic recrossing has essentially completely suppressed C-Br fission in bromo- propionyl choride where the splitting at the avoided crossing is of the order of 20 cm-’,we do see significant C-Br fission from nn* excitation in bromoacetyl chloride, and not all of these have to be from a first attempt at crossing the barrier adiabatically. Sorry I can’t be more specific. Dr. Olivucci said: The experimental results reported by the authors clearly demonstrate a competition between C- C and C-Cl fission in n-p* chloroacetone. However, the reported ab initio computations seem too crude to provide a firmdemonstration that this competition is due to reduction in the C-Cl rate constant from non-adiabatic effects.The major source of criticism arises from the way in which the authors define the C-C1 fission pathway and, in turn, evalu- ate the non-adiabatic recrossing rate for the reaction. In general, the rigorous determination of a reaction pathway involves the location of the minimum-energy reac- tion path (MERP) via the computation of the intrinsic reac- tion coordinate (IRC) on the relevant potential-energy surface. In contrast, the reaction coordinates investigated by the authors correspond to cross-sections along the C-Cl and C-0 stretchings and therefore do not involve full relaxation of all the internal coordinates of the system along the path. Obviously this leads to a rather arbitrary view of the n-p* reaction pathway and, in turn, to an incorrect evaluation of the magnitude of non-adiabatic recrossing rate for the reac- tion.Furthermore, one should recognize that, in general, MERP are usually located far from conical intersection (CI) points where one has large non-adiabatic effects. In fact, CI points appear as ‘local maxima’ on the potential-energy surface. Furthermore, because of the ‘double cone’ ground and excited state surface topology at a CI, small displace- ments of the MERP from a CI point usually lead to a large energy gap between ground and excited states and therefore to negligible non-adiabatic effects.In conclusion, in order to provide reasonable computa- tional evidence that the non-adiabatic effects reduce the reac- tion rate of the C-Cl fission, the authors should in my opinion demonstrate that the rigorously computed MERP does lie near a conical intersection (or weakly avoided crossing) point. Prof. Butler replied: The experiment measures how the C-C : C-Cl fission branching ratio changes with molecular conformation, finding that we observe a larger branching to C-C fission when we increase the fraction of gauche con-formers in the molecular beam. The calculations of cuts along the C-Cl reaction coordinate were undertaken to determine whether the larger branching to C-C fission from the gauche conformer was due to a larger rate constant for C-C fission in the gauche conformer or a smaller rate constant for C-Cl fission in the gauche conformer, or both.(The C-C :C-Cl branching ratio is kc-c/kc-c, so one must consider how each rate constant changes with molecular conformation.) Indeed, our calculations indicated that non-adiabatic recrossing of the C-Cl reaction coordinate could not explain the observed conformation dependence of the branching, as the recrossing reduces the rate constant for C-C1 fission more in the anti than in the gauche conformer. The increase in the C-C :C-Cl fission for the gauche conformer must thus be driven by a conformation dependence of the C-C fission rate constant. Your question implies that we were invoking a conical intersection along the C-Cl reaction coordinate.We were not; we invoked the importance of the conical intersec- tion along the C-C reaction coordinate, as shown schemati- cally in Fig. 7 of the paper. For the c-Cl reaction coordinate, the cuts along the C-Cl stretch at different C-0 bond lengths were meant to show that the crossing was, if anything, more strongly avoided for the gauche con-former for most of a wide range of C-0 geometries sampled as the C-Cl bond stretches through the avoided crossing. We do not think the C-Cl dissociative trajectories sample near a conical intersection. If you would allow me to reword your question, one might say that although by symmetry there must be a conical inter- section along the C-C reaction coordinate if the molecule retains a plane of symmetry as it dissociates, it may be that the potential-energy surface offers a lower-energy path to dis- sociation at non-planar geometries and that few of the trajec- tories attempt to cross the barrier to C-C fission near the conical intersection even if one excites the anti (planar) con- former [by, for instance, the C-(C-O)-C atoms distorting to a pyramidal geometry in the excited state].We plainly need both a potential-energy surface and a dynamics calcu- lation to address this question theoretically. I hope you will undertake a calculation of the minimum-energy reaction path along the C-C reaction coordinate (not the C-Cl one!). I would also be very interested in cuts that retain the plane of symmetry for the C-(C=O)-C atoms and the angle of the C-Cl bond with respect to the plane for the anti and the gauche conformers as you stretch the C-C bond.Our experiments on the closely related system of bromoacetone have measured the angular distributions of the C-C and the C-Br fission photofragments ;the observed anisotropy of the C-C products suggest that pyramidal distortion is not great during dissociation. I do not agree with your last comment that because of the ‘double cone’ shape of a potential-energy surface near a conical intersection, that the splitting between the upper and lower cone with small displacements becomes so great that non-adiabatic effects are negligible. There are countless ex- amples where this is untrue (try the dissociation of ICN or CHJ through a conical intersection, where the branching to both the adiabatic and the diabatic products are both significant).Indeed, the importance of non-adiabatic effects near conical intersections has long been recognized. (There are numerous papers by Truhlar, for example, on this subject.) Prof. Simons said: One way of establishing the differential photochemical behaviour of gauche and trans conformers of chloroacetone would be to record the photofragment excita- tion (PHOFEX) spectra under jet-cooled conditions. C1 atoms are readily detected using a REMPI scheme. A more general comment relates to the multidimensional nature of the potential-energy surfaces and their conical, or other kinds of intersection.It may be somewhat simplistic to consider surface crossing/recrossings only at low dimension- ality. Prof. Butler replied: I would very much like to see a jet- cooled photofragment excitation spectrum of chloroacetone. I hope you have plans to undertake this. There is one worry. We access the A” potential-energy surface due to Franck- Condon overlap with the inner turning point of the C-0 stretch (the equilibrium C-0 bond length is longer in the excited state) so the molecule has lots of vibrational energy in it. It may be that the high density of vibrational states and the short dissociation lifetimes will render the absorption spectrum structureless even under jet-cooled conditions. (Unlike in acetone, where we see very anisotropic photofrag- ment angular distributions from bromoacetone in the nz* absorption band.We assume that photofragmentation in chloroacetone also occurs quickly, and the measurement of b= 0 for C1 atoms from chloroacetone results from an average over molecular conformers, not from a long timescale for the dissociation.) I would also be interested in the anisot- ropy and branching in an argon-seeded beam where we could cool the conformer population to primarily gauche con-formers, but one must be very careful of dimer formation in these expansions. On your second point, I agree that showing a schematic reaction coordinate for C-C fission with just two degrees of freedom is simplistic. However, because we saw a marked dif- ference in the C-Br :C-C branching for the bromoacetone conformers (C-Br fission dominated in the anti conformer but could not compete with C-C fission in the gauche conformer) we focussed, in both bromo- and chloro-acetone, on the main geometry difference between conformers, the torsion out of the molecular plane.Where more detailed cal- culations on the C-C fission reaction coordinate have been possible (ref. 24) they indicate that the dissociation could sample geometries at the barrier where the C-(C=O)-C atoms are somewhat pyramidal, providing a way for both conformers to sneak around the conical intersection. Our anisotropy for the C-C fission products in bromoacetone put an upper limit on how pyramidal the structure becomes en route to dissociation; a of 0.7 for the C-C reaction products suggests the C-C bond direction, along which the recoil occurs, is not on average more than nine degrees from the planar geometry in the ground state when it dissociates.We have tried to focus here on the dominant difference that could cause the branching ratio to depend on molecular con- former, and have admittedly swept much of the richness of the multidimensionality of the problem aside to bring the primary message through as clearly as possible. I should note that many textbooks reduce the problem to only one degree of freedom and describe C-C fission as symmetry forbidden, where we know that it is symmetry forbidden only at a singu- larity on the potential-energy surface. Prof. Truhlar commented: In many cases the saddle point of a reaction is actually a local minimum on a ridge that forms a shoulder to a conical intersection.This is the case, for example, even for the very simple H + H, reaction. Thus one cannot always make a clean distinction between non-adiabatic behaviour at a conical intersection and non-adiabatic behaviour at a saddle point. Prof. Bordeo said: (A) What is the difference in the C-Cl and C-Br barriers that you calculate? (B) If you don't trust the difference between your calculated barriers quantitatively, why do you trust them qualitatively? Prof. Butler replied: (A) With a single reference C1 calcu- lation using an STO-3G* basis, the barrier to C-Cl fission in bromopropionyl chloride is just over 4000 cm-' higher than the barrier to C-Br fission.(we have only investigated the avoided-crossing seam by varying the C-0 bond length and stretching the C-Cl or C-Br bonds, respectively, freez- ing all other internuclear geometries at that of the equi- librium geometry in the ground electronic state. The number given is for the conformer with a plane of symmetry.) (B) Although the absolute barrier heights are difficult to estimate quantitatively, the relative barrier heights are much GENERAL DISCUSSION more easily estimated. In particular, before we undertook the calculations (which we undertook primarily to get a feel for the configuration interaction splittings at the avoided cross- ing near the two barriers) we knew that the barrier to C-C1 fission had to be of the order of 10 kcal mol-' higher than that for C-Br fission (see discussion in ref.lob). The barrier along the reaction coordinate for C-Cl fission results from an avoided electronic crossing, at stretched C-C1 geo-metries, between the nn"-da'a'') configuration and the npc, n*c-cda"a') repulsive electronic configuration. Likewise, the barrier along the adiabatic reaction coordinate for C-Br fission results from an avoided electronic crossing between the nz*c,o configuration and the riper n*C-Br(a"a') repulsive electronic configuration at stretched C-Br geometries. We can estimate the relative barrier heights to C-Cl and C-Br bond fission on the resulting A" potential-energy surface by considering the energies at which two npx o* (X-Cl, Br) con- figurations cross the nz*c-o configuration. Absorption spectra of bromoalkanes and chloroalkanes show that the npBr repulsive electronic state is much lower in energy o*~-~~ than the n n*c-cI repulsive electronic state in the Franck- fl!Condon regon (200 DS. 179 nm) and the repulsive configu- ration along the C-Br reaction coordinate correlates to a lower asymptotic limit (the C-Br bond is weaker), so the npBrQ*~-~~repulsive electronic configuration crosses the nn*c-o configuration at lower energies (ca.10 kcal or more lower) than the repulsive I+,,-, n*c-cI configuration does.(The diabatic potential is also a bit softer in the C-Br bond, further reducing the energy at which the repulsive C-Br diabat crosses the bound diabat.) Configuration interaction lowers the two adiabatic barrier heights from the energies at which the two repulsive surfaces cross the bound diabatic surface, but as long as the configuration interaction lowering of the C-Cl barrier is not 10 kcal mol- more than that for the C-Br barrier, the barrier to C-Cl fission will be higher than the barrier to C-Br fission.The barrier energy lowering ranges from a fraction of a kcal to 3 kcal, so it does not reverse the relative barrier heights. Prof. Borden began the discussion of Prof. Houk's paper: Do you think that calculations on butadiene dimerization, beyond the CASSCF/3-21G* level, will find that a con-certed transition state is lower than that leading to a diradi- cal? Have you performed such calculations? Prof.Houk replied: The trend observed with CASSCF/3- 21G, CASSCF/6-3 lG* and QCI calculations on butadiene plus ethene does suggest that higher-level calculations on the butadiene dimerization will cause the concerted transition structure and lead to very close diradical energies. This is what experiments on related systems also suggest. The CASSCF calculations without corrections for dynamical elec- tron correlation seems to overestimate the stabilities of dira- dicals as compared to concerted transition states. Rof. Nakamura said: There have been allusions to the intervention of single-electron transfer (SET) in the Diels- Alder reaction (Kochi). Since the difference between a con- certed reaction and a reaction involving SET followed by rapid in-cage coupling of the resulting radical-ion pair is difi- cult to decipher experimentally, it would be useful to address this SET issue theoretically.In addition, the SET process has recently been shown to be involved in the [3 + 21 cyclo-addition of a dipolar trimethylenemethane.' Have you con- sidered, or are you going to explore, this possibility? GENERAL DISCUSSION 1 E. Nakamura, J. Am. Chem. SOC., 1993,115,5344. Prof. Houk replied: We have not explicitly explored the SET process for the reactions discussed here, although the use of CASSCF calculations would allow such intermediates to be minima if they were favoured. The SET mechanism, to give a radical anion-radical cation pair, has been invoked in cases of strong donor diene or 1,3-dipoles reacting with electron-deficient alkenes.The Ei (donor)-E,, (acceptor) needs to be of the order of 5 eV or less in order to make SET feasible. Prof. Shaik addressed Prof. Nakamura : The experimental results I am aware of are those of Kochi who examined cycloadditions of tetracyanoethylene to 9,lO-disubstituted anthracenes, and found a correlation between the Gibbs energy barriers and the charge-transfer transitions of the cor- responding reactants’ charge-transfer complexes. In these cases the ionization potentials and electron affinity allow, in principle, an electron-transfer process. Nevertheless, even in these cases one does not observe electron-transfer products, but rather cycloaddition products.We have discussed these kind of problems in the past in terms of curve crossings of the type discussed in my present paper on the ACS paradigm [e.g. Fig. 4(b) and (c) there]. What happens is a curve crossing which involves a significant mixing of the charge-transfer (CT) configuration into the curves of reactants and products.’ Thus, despite the dominance of the CT configuration in the TS region, the strong VB mixing binds the two reactants strongly and leads to cycloaddition rather than to electron transfer. The fact that Kochi observes correlations of reac- tivity with charge transfer excitations is reflecting therefore the role of the CT configuration in the avoided crossing and has little to do with an actual electron-transfer reaction.1 For a description of the reactants’ and product curves for allowed cycloadditions, see for example ref. I@)-(e) and 40 cited in my paper in this Symposium, as well as A. Ioffe and S. Shaik, J. Chem. Soc., Perkin Tmns. 2, 1992,2101. Prof. BaUy said: (A) You say in your paper that on dimer- ization of cyclobutadiene (CB) the transition state of the Cope rearrangement of the syn dimer is reached. However, as pointed out correctly by you, the Cope rearrangement of the syn dimer is not observed due to formation of cyclo-octatetraene (COT) by a lower-energy path. So why is COT not observed upon CB dimerization, more than enough energy being available for this process? (B) Given the substantial differences between the (CASSCF) predictions with the 3-21G and 6-31G* basis set (for absolute and relative energies, especially in the CB dimerizations), what confidence do you have in the capability of your model to predict the reaction path for CB dimer- ization correctly? Do you think inclusion of dynamic corre- lation could alter the picture significantly? Prof.Houk answered: (A) Perhaps because the reactions in general are studied in solution or in low-temperature matrices, where the energy can be readily dissipated. (B) I do think that dynamic correlation corrections are necessary in order to obtain reasonable energies. It is possible that a concerted mechanism for the syn dimerization could materialize upon inclusion of dynamical electron correlation.Dr. Walsh said: On the question of cyclobutadiene chem- istry, I would like to comment that we have carried out extensive kinetic studies of hydrocarbons in the C,H, manifold’ (uiz. measurements of activation energies and of energy release). We would anticipate that in the gas phase, while the initial products of cyclobutadiene dimerization would be syn-and anti-tricyc10[4.2.0.0~~~]octa-3,7-diene, the energy release would be sufficient to cause isomerization to cyclooctatetraene and its breakdown products. The gas pres- sure would determine the extent of stabilization of specific C,H, products. To our knowledge such studies as have been carried out have not addressed the issues of energy release and product-yield pressure dependences.1 K. Hasseruck, H-D. Martin and R.Walsh, Chem. Rev., 1989, 89, 1125. Dr. Walsh continued: I would like to ask you, and indeed other theoreticians, a question about the accuracy of your calculations. As an experimentalist who has more experience of measuring activation energies, I am used to quoting uncer- tainties (precision). Depending on the experiment in question these may vary; however, a typical kinetic study of hydrocar-bon thermolysis (or cycloaddition) would probably give f4 kJ mol- ’,if reasonably carefully carried out. Theoreticians however, often do not assess the accuracy of their (ab initio) calculations but rather cite ‘a certain level of calculation’ with ‘a certain basis set’ and argue as you, Prof.Houk, have done in your paper that this gives results in agreement with experiment. But we know that improving the basis set and level of calculation can often change the answer, particularly when alternative mechanisms are being com-pared. How do you judge that the calculation is reliable and that further refinements will not change the outcome? Prof. Houk replied: The precision is high: the uncertainty in calculations is essentially zero; that is, they may be repro-duced exactly to many decimal places. However, the accuracy may not be very good. We have documented in our Ange-wandte Chemie article in 1993, and to a lesser extent in this Symposium, how we can gradually converge on the experi- mental activation energy by better calculations.Many times, for reactions of the size that organic chemists like to study, it is not possible to perform calculations at a high enough level to be certain they have converged to a final answer. This is why comparisons with experiment are often done. For suffi-ciently small systems, there are methods, such as Pople’s G1 and G2 methods, which are prescriptions for obtaining ener- gies to within +2 kcal mol-l of the exact experimental result. Dr. Williams said: Activation energies are not the only quantity of interest for comparison of theory with experi- ment, for example, kinetic isotope effects are extremely important experimental probes for transition-state structure. Could you please comment upon the accuracy of your com- puted isotope effects, particularly in regard to the choice of basis set and the effect of electron correlation? It would be interesting to know how the value of the imaginary reaction- coordinate frequency depends upon the method employed.Prof. Houk replied: The predicted isotope effects do vary as a function of computational level. Some examples for the butadiene-ethene reactions are shown in Table 1. The forming bond lengths are also shown, to indicate how the position of the transition state is changing. The isotope effects do vary over a rather large range. The RHF results, which give later transition states, give larger Table 1 Predicted isotope effects for the butadiene-ethene reaction k”,/kD,computational forming bond level length/A 1,l-diene 1,l-dienophile RHF/3-21G RHF/6-31G* M P2/6- 3 1G* MCSCF/6-3 1G* 2.210 2.202 2.286 2.223 0.91 0.92 0.94 0.94 0.91 0.92 0.94 0.96 inverse isotope effects than the correlated wavefunctions, which give earlier transition states.Nevertheless, the mech- anistic implications are clear when concerted and stepwise mechanisms are compared.’ J. Storer, L. Raimondi and K. N. Houk, J. Am. Chem. SOC., in the press. Dr. Nguyen said: My question is related to the results pre- sented in Fig. 2 of your paper. Accordingly, the closed-shell quadratic configuration interaction, RQCISWT), method gives the best energy barrier compared with the experimental result. The CASSCF method tends to overestimate this quan- tity. This shows the importance of dynamical electron corre- lation.There is, however, a difference of ca. 4 kcal mol-’ between the results obtained by UQCISD(T) and RQISD(T) methods. Such a large difference is alarming! How would you explain these results? I wonder whether the UHF references are heavily contaminated. On the other hand, are closed-shell single-reference wavefunctions adequate for treating con-cer ted cy cloaddi tions ? Prof. Houk replied: Indeed, dynamical electron correlation is needed to obtain good energies. Yes, the UHF results are highly spin-spin-contaminated, ca. 50% triplet for the diradi- cal, but mostly singlet for the concerted pathway. RHF calcu- lations are quite good for concerted pathway geometries: we know that now by ample experience on many allowed reac- tions.Prof. Tomasi addressed Dr. Walsh: I would like to add my comments to the question you raised. The primary goal of theoretical chemistry is that of giving a picture, an interpreta- tion, and not that of checking the numerical outcome of experiments within their error range. Anyway, the theoretical foundations and the technical methodologies (in perspective) to reach the accuracy typical of good level experiments are available if the material system under scrutiny is of ‘limited’ size (as, for example, the molec- ular systems considered in the Houk paper and in many other papers presented in this Symposium). This level of accuracy has not yet been reached, but it is within the limits of the present approaches and surely will represent, in the not too distant future, an interesting alternative to experiments, especially in cases for which experimental measurements are difficult to perform.The situation is not so clear, in my opinion, for systems of ‘large’ size. The computational methods theoreticians employ for the study of phenomena occurring in solution or in complex biomolecules are inherently approximate and also their theoretical layout is far from being satisfactory (let me quote, as example, the status of temperature in the molecular quantum-mechanical formalism). Much work must be done GENERAL DISCUSSION in this field: ‘interpretations’ are currently proposed, with remarkable success, but the formal connection with a com- plete and exhaustive theory does not exist.Prof. Borden added: While I agree that the goal of theory is qualitative description, it is also true that calculations have become capable of quantitative accuracy. There are now many instances where theory has been able to correct experi- mental results or, more precisely, their interpretation. Rel- evant to Prof. Houk’s talk, his QCISD(T)/6-31G* results show that at this level of theory the activation energy for ethene and butadiene cyclohexene is calculated with quan- titative accuracy (ie. within 1 kcal mol-’ of experiment). We have obtained results of similar quality with CASPT2N and QCISD(T)/6-3lG* calculations on the Cope rearrangement and cyclobutene ring opening. However, different reactions may require different levels of theory.For example, calcu- lations of relative C-H and 0-H bond strengths at this level are in error by ca. 10 kcal mol-l. Dr. Walsh said: If Prof. Tomasi is right, then because we have quantum theory and because we have the Woodward- Hoffman rules to give us the picture, we do not need any- thing else. Theoreticians would soon be out of business if the only goal is pictures. I believe, like Prof. Schleyer, that quan- titative prediction is at least equally important. As to whether it can correct experiments, i.e. point out when they are wrong, I accept Prof. Borden’s point that it certainly can, and in cases known to me, it certainly has done. Thus I do not wish to imply that experimental results are ‘holy’, and do not need repeating (as Prof. Schleyer implied). There are good and bad experimental studies just as there are good and bad theories. Experimentalists argue amongst themselves just as much as theoreticians. Experimentalists need theoreticians to guide their vision, but theory will quickly become anaemic if it does not direct its goal to predicting the outcome of experi- ments. Dr. S. Wilson communicated : Basis-set truncation effects are widely recognized as the main source of error in contem- porary molecular electronic structure calculations,’ a fact which is well illustrated by the results presented in this paper. Huzinaga’ has suggested that calculations in which the basis- set truncation error is not controlled should be termed quasi- empirical. Recently, we have developed basis sets which are capable of delivering energies to within a few pE, of the exact To date, our work has been limited to the Hartree- Fock model for diatomic systems but with the availability of increasingly powerful parallel processing computing machines able to carry out matrix operations with high efficiency’ we envisage the emergence of applications of a comparable accuracy to polyatomic systems, to calculations taking account of correlation effects6 and perhaps even rela- tivistic effects’ over the next year or so. 1 S. Wilson, Adu. Chem. Phys., 1987,67,439. 2 S. Huzinaga, Comput. Phys. Rep., 1985,2,279. 3 D. Moncrieff and S. Wilson, J. Phys. B, 1993,26,1605. 4 D. Moncrieff and S. Wilson, Chem. Phys. Lett., 1993,209,423. 5 D. Moncrieff, V.R. Saunders and S. Wilson, Supercomputer, 1992, 50,4. 6 B. H. Wells and S. Wilson, J. Phys. B, 1986,19, 2411. 7 H. M. Quiney, I. P. Grant and S. Wilson, J. Phys. B, 1990, 23, L271.

ISSN:0956-5000    

DOI:10.1039/FT9949001605

出版商:RSC    

年代:1994

数据来源: RSC